Most of my shows are only one-day affairs. I take a 6 gallon water can per day per horse. The 6 gallon water cans are basically blue gas cans and can be bought anywhere, I buy them at Dover.
One of these:
https://www.doversaddlery.com/blue-plstc-water-can-60-gal/p/X1-27704/
I put the container in the corner of my trailer’s dressing room with my buckets and bathing stuff (20 qt bucket, 6 qt bucket, sponge, sweat scraper, small sponge - all put inside the 5 gall bucket and strapped to the 6 gallon can).
Most of my horses might drink a gallon – if that – at shows, so the water is mostly for cooling them off and wiping down tack.
You can transport the water in the bed of the truck instead, if you don’t have a dressing room. Some trailers even have a built in watering container that can hold up to 100 gallons.