I think the root cause of this is stress, so it's worth working on making the loading/travel process as stress-free for her as possible. Practice loading and not going anywhere, and make sure the trailer/lorry is bright, airy, and put down some bedding. Make sure she has enough room to move her feet, as well to lower her head - this will help her find her own balance. Other than that, if she's actually happy to load and travel, there's not much you can do. Most travel rug options will either be light summer sheets, light fleeces with wicking properties to draw the sweat away from her skin, or mesh type rugs, which work by trapping pockets of air next to her skin. If she sweats in *any* kind of rug, then all you can do is factor this in to your plans - carry plenty of water so she can drink and not get dehydrated, sponge her down and walk her around when you arrive at the other end. It may well just be one of those quirks you have to live with, but try a few of these ideas and see how you get on.