There are very few descriptions of ships in the Lord of the Rings. The ship at the very end of the story, for instance, is simply described as "a white ship". The only hints to its form or function are that it had several sails, which were drawn up, as opposed to being unfurled: "and the sails were drawn up, and the wind blew, and slowly the ship slipped away down the long grey firth". Bilbo's verses on Eärendil only tell us that his ship was built of timber, and "her prow was fashioned like a swan", although since hobbits in general aren't the most nautical of creatures, this lack of detail isn't all that surprising. The ship he pilots through the heavens, though, is single-masted. In the Silmarillion, rowers are referred to and ships are rowed, suggesting galleys.
Even the description of Númenor and the tale of the mariner's wife in Unfinished Tales give very few details on the actual ships of the Númenorans. The only passage that stands out is in Aldarion and Erendis:
So it was that ere long he turned again from forestry to the building of ships, and a vision came to him of a mighty vessel like a castle with tall masts and great sails like clouds, bearing men and stores enough for a town. Then in the yards of Rómenna the saws and hammers were busy, while among many lesser craft a great ribbed hull took shape; at which men wondered. Turuphanto, the Wooden Whale, they called it, but that was not its name.
The description of a ship like a tall castle with many masts recalls a medieval carrack, but other than that and the mention of constructing the frame first, there isn't a lot to go on.
As for the Corsairs of Umbar, we have the brief description of the fleet making its way up the Anduin:
And looking thither they cried in dismay; for black against the glittering steam they beheld a fleet borne up on the wind: dromunds, and ships of great draught with many oars, and with black sails bellying in the breeze.
- The Lord of the Rings, book V, chapter VI
By dromund I assume Tolkien means dromon, a Byzantine galley. The reference to many oars makes it clear that the other Umbar ships were also large galleys of some kind. As a general note, if oared ships capable of clearing the delta of the Anduin were considered "of great draught", this suggests that ships at the time of the War of the Ring weren't very large by the standards of the age of sail.
Another source on the ships of Middle-earth is Pauline Baynes's map, prepared according to instructions from Tolkien. The accompanying article only cites Tolkien's opinion on the colors of the sails, which is, frankly, probably the most useless detail they could have included. But the ships on the map are clearly medieval: there's a galley with black lateen sails, and what looks like an early caravel just off the coast of Umbar. Several other ships have the distinctly high fore- and aftcastles of stylized medieval ships. The two ships seen off Mithlond are also highly stylized, but call to mind Northern European ships with their single square sails and low, symmetrical hulls.
Luckily, the Tolkien Society has provided a transcribed version of the annotated map, allowing us to read Tolkien's instructions on the ships. In the Bay of Belfalas, Ms. Baynes was instructed to draw "vessels of varying sizes, from 3 masts to single". Off Cape Andrast, Tolkien has suggested "9 weatherbeaten galleons", adding "as large a pre-steam vessel as can be drawn i.e. Columbus type". This instruction is nonsensical, and makes it clear that Tolkien had very little idea of ships or sailing. Columbus's ships were not galleons, or for that matter anything near as large as pre-steam vessels could be. Taken literally, Ms. Baynes would have had to draw either massive Spanish galleons or Napoleonic men-of-war, neither of which can be easily squared with the descriptions of ships in Tolkien's texts. The part of the instruction she obeyed was "Columbus type", drawing several carracks, which seems to have been approved by Tolkien (sadly, his Letters don't seem to document any nautical discussions). Off Mithlond, Tolkien requested "single masted elven vessels" as well as "small boats any shape going eastwards", and "elven ships small".
To sum up, then, elven vessels seem to have been small single-masted galleys. The only elf-ship described as having more than one sail was the very last of them, and it's not clear whether there were several masts or if Círdan had incorporated a topsail in the design, or maybe a bonnet. Similarly, the ships of the Corsairs of Umbar were larger galleys, possibly similar to ancient Mediterranean war galleys. This leaves us with the Númenoran shipbuilding tradition. As this seems to have been based on elven examples, we can conjecture that Númenoran ships will have been galleys or possibly something like longships, to account for their seagoing qualities. Combining the account in Unfinished Tales with Ms. Bynes's illustrations, it's possible to speculate that the Númenorans developed something very similar to carracks, which would have given them a great advantage over Corsair galleys in open waters. These carracks still won't have been too large, though, if the galleys coming up the Anduin were of particularly deep draught.
So let's see what the game designers and artists gave us.
The Dream-chaser's Fleet
Technically, the Dream-chaser appears to be a barque: there are two square-rigged masts and a gaff-rigged mizzen mast. Or, alternatively, if the fore-and-aft sails are actually on the mainmast, it's a brig, but I'm inclined to think that would make them unfeasibly large. This is basically an 18th-century hull and rig, with the split topsails and topgallants dating it to the end of the 19th century. At first glance, it looks more like a 19th century clipper than any ship I could easily imagine existing in Tolkien's world. The card identifies it as an elven-ship of the Grey Havens, but the appearance of the ship is impossible to reconcile with any descriptions of elf-ships in Tolkien's texts.
The Dawn Star, on the other hand, is a Gondor ship. The square bow, high aftcastle, crow's nest and oars give a robustly medieval impression, and based on Ms. Baynes's map and Tolkien's texts, this is a fairly good impression of what a top-of-the-line Gondor ship of the approximate time of the Lord of the Rings card game might have looked like. I'd personally suggest that three masts might be a bit much, but given our dearth of information, this is a matter of taste.
Confusingly, judging from the shape of the hull and the mizzen lateens, the next elven-ship is fairly obviously a galleon. The iconic ship of the Spanish empire, the galleon is a considerably larger and later ship design than anything Tolkien ever described, but also centuries older than the late-19th-century Dream-chaser. It's nothing like the small, sleek elf-ships of Middle-earth.
The Silver Wing appears to be rigged as a hermaphrodite brig, with square sails on the foremast and a gaff-rig on the mainmast. After the two medieval ships, this is a representative of the golden age of sail; again, centuries off anything to be found in Tolkien's works. Even the two Gondor ships come from entirely disparate eras.
The Umbar Navy
I'm not really quite sure what's happening with the sail in the picture there. Looking at the shrouds, though, the mast seems to be quite a bit higher, and there appears to be a second, more substantial mast further aft. The shape of the hull and the oars suggest a large galley of some sort. Two banks of oars are visible; if the third line of ports are also for oars, this would technically be a trireme. In other words, this is a fairly good representation of the kind of ship Tolkien described in the Lord of the Rings.
A smaller version of the Corsair Warship, the Light Cruiser almost resembles a longship rather than a Mediterranean galley, except for the twin masts and sailplan, which appear to be an unusual configuration. The deckhouse is also strongly reminiscent of the Med. The ship is broadly in line with both the Warship and Tolkien's text.
Finally, the low hull of the Scout Ship quite strongly suggests a Scandinavian "dragon-ship", although the unusual split sail is an innovation.
The Corsair ships, then, are quite faithful to Tolkien's writings, but with the exception of the Dawn Star, the ships of the Dream-chaser's fleet are just a mess. A galleon, a hermaphrodite brig and a 19th century barque coexisting uneasily with a medieval carrack and some ancient Mediterranean galleys with very unusual sails. At a guess, the artists were told to draw "a sailing ship", which produced this melange. It's sad that the titular ship of the current adventure pack cycle is the worst offender.
The quest in the Grey Havens that the ships are used in is Voyage Across Belegaer, where the heroes are attempting to outsail a fleet of Corsairs and reach Atalantë. Given that the action happens in the open ocean, the ships of the Dream-chaser's Fleet as depicted on the cards would have no trouble whatsoever sailing clear away from the Corsair galleys. Looking at the sheer amount of canvas the Dream-chaser, Nárelenya and Silver Wing can hoist, under any kind of wind they'd simply vanish over the horizon. It's possible the Dawn Star would have a slightly harder time of it, but it should still be able to outsail anything in the Corsair fleet. The only conditions under which the Corsairs could bring the players' ships to battle would be in a flat calm, where their banks of oars would give a decisive advantage. Bad weather would also disproportionately impact the Corsairs, as their considerably less weatherly ships might be swamped and sunk by seas that the Dream-chaser fleet would easily ride out. So if the ships in any way resembled the art, the scenario they're used in would make no sense.
On the other hand, if the ships of the Grey Havens are one-masted elven longships, possibly accompanied by Gondorian galleys or light carracks, then the quest begins to make a whole lot more sense. The elven ships would probably be smaller but more nimble than the Corsair galleys, whereas the Gondor ships can spread more canvas. At close quarters, however, the larger crews of the Corsair ships could overrun the Dream-chaser fleet, meaning that in order to escape the Corsairs, the Dream-chaser fleet would have to work diligently to stay on their best point of sailing. Bad weather might be to the advantage of the Corsairs in forcing the smaller elven-ships to ease off.
So to sum up, the sailing quest in the Grey Havens would make sense for the kinds of ships Tolkien actually described, but fails completely with the ones actually depicted. That makes this a unique case in the Lord of the Rings card game where we can legitimately complain about the art! For my money, the Grey Havens is still the best deluxe expansion in the whole game: the quests are great, the player cards are pretty sweet and the art is lovely. The only exception is the ships, which I do have to say I'm very disappointed in.