Hydration!! Water is a MUST even if she doesn't like to drink a lot of it. If she doesn't like drinking water, get those Propel drink packets and add those to bottled water.
Water is THE way to prevent heat stroke (had that pounded into my head in the Army
Someone else mentioned having a t-shirt or tank top that she can wear around. Great idea. It will also help to keep her show shirt crisp and clean for the actual show.
For the horse, lots of clean water (bring some from home if the horse hesitates to drink "strange" water). If he/she is all spiffed up for a show, you can still take a lightly dampened sponge and wet down the belly without messing up the prettiness. Try to keep the mane off the neck if you can. Shade would be nice if available, so try to tie him/her up on the shady side of the trailer.