A friend of mine has a horse with the same problem. She's an older mare, in her late teens, and has been routinely trailered and shown for most of her life - loads like a dream, with minimal barn/herd sourness, just an all around good horse. She sweats like mad, every trailer ride.
Her owner just lives with it - it hasn't changed in 15+ years of trailering, and doesn't look likely to change any time soon. They get to shows early enough to walk her dry.
If it's a very green trailer-er, I'd say positive experiences will go a long way. In the case of my friend's mare, it's just one of her quirks.
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown