I used a two-horse stock trailer for 14 years and always put shavings in
it. I never had a problem with them blowing around. I did keep a
mask on my horse, but it was in case any foreign object blew into the
trailer. Since Cheers pees copious amounts in the trailer, even
when we trailer 20 minutes, it was a necessity. In the last couple years
I've been using the wood pellet shaving that you dump water on and they
expand. I love them! They're very easy to clean out, just pick the
poop and the major wet spot, then mix in a couple double handfuls of
fresh pellets. By the way, I have heard that straw actually has more
dust particulates than shavings, plus it's not absorbent. I've seen people
arrive at rides who put straw in their trailers, and the horses are standing in
a wet stinking mess after only a couple hours.
As far as wrapping....I used to ice Cheers for about an hour, then put
Ice Tight, wet paper (like grocery bags), pillow wraps and standing wraps.
I feel it did help keep him from stocking up. I also hand-walked him a lot
after the ride. I don't do any of that with my new horse since we've only
done LDs so far. I'll decide whether to do it or not when we switch to
50's. One deciding factor is if he'll let me pull myself up from squatting
down by using his tail like Cheers did!