I've never had a problem. Of course like anything with horses... its not to say that it couldnt cause problems. But the rain does come in and get my mats wet. I don't uses shavings. But even when I have had to make quick stops (which doesnt happen to often... I give myself tons of room... especially when its raining, but it does happen.) my horses came out of the trailer fine.
Prime example... we did a demo at my old HS and it started pouring rain. So the mats got wet... and of course we were riding at the time... so the horses were soaked when we loaded them. One the way home someone cut in front of me cause they needed in the turn lane that was blocked. So they had to lock up their breaks... and I had to lock up mine because I had cars on both sides of me. And neither horse slipped. If that makes you feel any better.
Many people have sighed for the 'good old days' and regretted the 'passing of the horse,' but today, when only those who like horses own them, it is a far better time for horses. ~C.W. Anderson