I assume this trailer has a steel frame? This will most likely be a temporary solution because winter salt will destroy the frame and crossmembers. Knowing this, I would not go overboard. While sealing the floor will keep out moisture, it will also prevent it from drying. Are you worried about melting snow from a sled or outside water getting in? The plywood floors dry quickly. I am not sure I would put a ton of effort or money in a floor coating. Keep a push broom in your wagon and sweep out all of the snow you can.

I have both cargo and snowmobile trailers and have used the cargo to move a sled when needed. It's not my preference, but I realize there are other needs and circumstances.

 

I used a 6x12 enclosed trailer for the first time last year. I laid down a heavy duty tarp to help protect the floors (track mats and glides went down overtop). I was hoping this would make it easy to remove any snow/melt that fell off the sled. But what I didn't anticipate is that after every ride, the sled would melt enough that I had about 1-2 inches of water that would come off the sled. This would pool in the back corner and freeze on me (I park the trailer on a slant so water runs back towards the ramp door). Any time I went out i'd remove as much snow and ice as I could from the trailer, but it just built up more and more over time.
I'm thinking about installing a shower floor drain so that this melt water can leave the trailer to help with my issues - going to find a metal one that I could heat up if it ices over...
To answer your question though, it's my opinion that unless you let the sled cool off completely before loading it, you will always have water issues in your trailer. Seems like most people just let the water be absorbed into the wood. So anything you do to protect the floor should help increase the time before you need to replace the floor.

 

I have been using a 7x16 enclosed trailer for hauling sleds since 1988...The most recent new trailer purchase was in august 2020, that was either my 9th or 10th new one, cant remember...lol...Never had anything on the floors of any of them, and never had any issues due to carbides, picks, or water/ice...I have had Pace, United, Haulmark, Royal, Discovery...Cant give a recomendation on any of them...BUT...The worst of the bunch was by far the Haulmark...The new COVID pricing is insane...My exact trailer now is $3000.00 more than I paid last year...

 

If you don’t care about cost, get some commercial rubber coin flooring. I picked up a new 7x14+2 enclosed this year and did the floor with the rubber coin and super track guides. Looks fantastic in person and seems like it will be super Durable