While you can easily fit them in that trailer, those trailers are NOT necessarily waterproof. I have had them leak on me multiple times. I strongly suggest putting a tarp on the bottom, games on that, and then put a tarp over it as well. You don't need to go crazy since you won't get driving water like you would in an uncovered trailer plus your tarps won't be in the wind causing issues that way, but it makes sense to take a few extra steps to keep your stuff dry.
Jaz