Thanks everyone. Sounds like mostly a judgement call. It is an enclosed trailer, but still, I imagine it could get breezy in there regardless. Plus the walls aren't insulated so they would transfer the cold quickly.
I will never, ever tie my horse in a trailer unless for some weird reason I don't have a choice. First, she sometimes has the trailer to herself, so she can turn around and stand however she likes (usually backwards and/or on an angle). Second, if she does fall for whatever reason, her head is stuck way up there while her body is way down there. Scary. Would you leave a horse tied and walk away? Nope. Same reasoning here for me. I know that it is a preference thing. This is mine. Thirdly, in case of an accident, same deal with the head being tied - way to scary if the head is in one place while the body is flipping all over.
I used to wrap her legs, but honestly never found a reason for it. She trailers well, never has scrapes, never any problems with her legs at all.
I drive like an absolute turtle when I trailer horses anyway. I'm always the last one in the convoy! :)