Maybe back around 1975 or 76ish, was boarding in So Cal at a big, multi trainer/discipline equestrian center during another “unprecedented” drought. Limited or no lawn watering, no car washing etc.
Barn shut down the line to the wash racks and all but one faucet per shed row (stalls had auto waterers). We brought soaking wet towels and sponges in a 2 or 3 gallon tub with a lid from home, filled it about half up with home water with a little alcohol or witch hazel. Just rubbed the horse with those, put a dab of soap on one for socks and such. Then filled our allotted one bucket with clean water and used clean towel/sponge to rinse.
You can actually do a white tail this way too but if you keep it in a single braid it stays cleaner.might even look into a tail bag.
You are stuck with the dusty arena though. We actually trail rode or worked on any flat place we could get a couple of big circles going in. Nothing died being forced to work out of the carefully manicured footing that used to be watered twice daily.
This whole thing reminds me of something I was told when I first started…the hose is NOT a grooming tool. Matter of fact when I started, bathing was kept to a minimum, many felt it was detrimental to just turn the hose on then-we used buckets and sponges. I’m not sure it’s wrong since you can’t really check everything about the horse after it works standing 3’ away waving a hose at it for 2 minutes instead of sponging over every inch including the nooks and crannies…which actually only takes about 5 minutes of your time.