Interesting question. I would also favor linoleum, because it will contain meltwater coming off of snowy boots. Any other type of flooring will have cracks that could let the water penetrate to the subfloor. Just wipe up the water with a rag, and you're good to go.
Linoleum is not easy to cut precisely, however. So you would need baseboard, probably quarter round, to cover the gaps. Bear in mind that MDF baseboard (the most common material these days) can deteriorate when exposed to water.
We have floating vinyl plank (not glued) in our stick house -- it does not make a clicking noise, but it feels different than glued flooring. In either case, you would not want to expose vinyl flooring to puddles of water -- it is not really water-proof. It is water-resistant.
I wonder if it makes sense to have a moisture barrier installed before you put in the flooring?
If you want to get fancy, there are some types of vinyl plank that provide some insulation -- I think Coretec does. It has a thick cork backing. That would keep the trailer warmer in snowy conditions.
2012 Fun Finder X-139 "Boondock Style" (axle-flipped and extra insulation)
2013 Toyota Tacoma Off-Road (semi-beefy tires and components)