Things are buoyant if they can displace water (or, liquid) equivalent to their own weight (well, mass, but I'm not doing the science hard enough and don't want to suggest that I am). Specifically:
In simple terms, [Archimedes'] principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g.
Wikipedia says that liquid nitrogen ("LN2") has 80.8% the density of liquid water. I'm not an expert, but that doesn't seem like a big enough difference to make it impossible for a vessel to displace its own weight. The Wikipedia article for buoyancy even has a photo of a coin floating on liquid mercury.
I'd guess that vessels built to sail on LN2 would probably be wider than ocean vessels. My intuition is that this increases the surface volume of the vessel relative to its mass, increasing its buoyancy to counteract the weaker upthrust from the less-dense LN2.
NuclearHoagie addresses the general problem directly and more succinctly:
It's never impossible for a vessel to displace its own weight in fluid, you just need to make it big enough... This is totally feasible, as the weight of the boat is mostly related to its surface area, which increases more slowly than the volume due to the square-cube law.
("NuclearHoagie" is a submariner's handle if ever I saw one, and buoyancy is a core concept for anyone who lives in an underwater metal tube filled with atmosphere.)
Of course, let's not forget that LN2 is pretty cold stuff. That is going to pose some fun engineering problems when it comes to the hull, and to locomotion. If the planet has no atmosphere, any sailing vessel will need to generate thrust by interacting with the liquid. That could mean oars, or a turbine. Or, because LN2 is so cold, perhaps a small heat source aft could generate thrust by causing rapid, localized expansion of the LN2 to push the vessel forward.
ETA: I think the temperature thing is going to be a huge deal. Sailing on an ocean of cryogenic fluid is going to pose unique problems that will definitely kill your passengers and destroy the boat, even if it continues to float.
Wikipedia says LN2 clocks in at -196 C, which is fantastically cold. Why is this a problem? Space is cold, so why isn't it a problem in space?
Consider wind-chill. If the air flowing past you is colder than your body, it will carry heat away from the surface of your body. The reason it feels colder when the winder is stronger is because stronger wind is just a greater quantity of atmosphere whipping past you per unit of time, which means more atmosphere to carry heat away from you faster. If the air temperature is 0 C, powerful winds can't cool you to below 0 C, but they will cool you to 0 C faster than if there was no wind.
Yes, space is cold, but space is also a vacuum, which is just to say: there is no stuff floating around in space that can absorb your heat energy. So, you'll eventually freeze in space, but it will take a long time. Long enough that we can easily counteract it with insulation and conventional heat sources. (And, also, humans in space do float around because they are weightless. That doesn't make them immune, but it does mean the air inside the spaceship helps shield them.)
Wind is just atmosphere in motion. Atmosphere is just very thin soup. Ocean is very thick soup. An ocean of LN2 is pretty thick soup that is also stupendously cold. If the vessel is not moving, the LN2 it's touching will absorb some heat from the ship and warm up. As it warms, it will absorb additional heat more slowly, until it reaches equilibrium with the hull. (Or, until the LN2 undergoes a phase change, but let's ignore that and pretend the LN2 will magically stay liquid no matter its temperature.) If the vessel is moving, it will continuously move away from the warmer LN2 and come into contact with LN2 that hasn't been warmed yet. It's the same principle as wind-chill. If the vessel is moving faster, that means more LN2 is flowing past the hull per unit of time, carrying heat away from the hull faster.
An ocean of LN2 is essentially a bottomless energy-void that craves heat. It will relentless drain all the energy out of the vessel. The faster the vessel moves, the greater the drain. First, the hull will be cooled down to -196 C. That will happen very fast. Then, anything in direct contact with the hull will be chilled to -196 C, and so on and so forth, until every object is frozen solid that is being held aloft by the hull.
So, where is your human passenger? Sitting on a cushion on a wooden chair with rubber feet, on the floor of the bridge? Where is the bridge? Is it a small enclosed structure standing on heat-resistant risers on the deck? Is the deck in contact with the hull?
Well, then, unless the passenger is somehow floating above the chair like magic, that's precisely the route by which the LN2 ocean will leech the heat out of her/him: hull > deck > risers > bridge floor > rubber feet > wooden chair > cushion > space suit > clothing > skin > cryogenically frozen corpse.
Okay, let's put the human on an indoor swingset hanging from the ceiling by a very thin -- but extremely strong -- non-metallic wire. It's just one thin wire, right?
I think it won't make much difference. Unless you can insert a barrier across which no heat is transmitted, the human will freeze to death, and pretty quickly.
Any artificial heat source will also be drained. Even a blazing housefire will go out if you can just lower its temperature enough. Many kinds of electrical battery do not work when very cold. I think radioactivity might be unaffected, but we harness that energy by heating water to steam which then drives a turbine -- and I'd guess that the cooling effects of the LN2 would be more than enough to keep the water frozen solid unless you pulled all the control rods out of the reactor and let it go critical. That would probably melt the ice, just before vaporizing the reactor and the human and the boat.
And none of this addresses the likelihood that the structural integrity of some parts of the boat will fail when they get cold enough, which could lead to some kind of partial physical collapse, bringing the human in contact with the deck or hull and thus much closer to the LN2.
And none of this depends on the planet having an atmosphere. It's heat transfer through indirect physical contact with the LN2 via the hull and everything the hull supports.