Nothing beats hosing it off with warm water. Take a container of hot water from home with you, and add something like this.
If you are handy, or have a handy friend, here is a self-contained battery powered water hose pump I built to take to shows and trail rides. It sucks water from a container via a short garden hose, then I spray it out via a 10 foot lightweight 1/2 inch diameter garden horse hose and nozzle. I use a 7.5 gallon container of warm water, but any size source container will work. The RV pumps recommend a 1/2 diameter garden hose rather than the more typical 5/8 inch diameter ones for better pressure and spray.
Parts include a 12 volt powered water pump, sized and made for use in RV bathroom plumbing. I used a name brand Shurflo from Amazon for $75.
https://www.amazon.com/SHURflo-Revolution-Water-Pump-4008-101-A65/dp/B010TKMK4O/ref=sr_1_3?crid=2R0QPV13OCCB6&keywords=shurflo%2Bwater%2Bpump%2B12v&qid=1675474000&sprefix=shurflo%2Bwater%2Bpump%2B12v%2Caps%2C87&sr=8-3&th=1
A 12 volt lightweight lithium iron phosphate battery, Batter Tender brand, also from Amazon. It is no longer available on Amazon, but similar battery options are around $50.
An on-off switch and a plastic container, bought from Tractor Supply, plus a couple of PVC connectors and fittings to connect garden hose ends to the pump inlet and outlet. I also wired in a Battery Tender lithium battery charger, so everything stayed in one place.
A 7.5 gallon container is enough to give a horse a nice warm rinse down after a workout, with good but not fire hose pressure, and the battery charge seems to last forever. I just weighed the pump on my feed scale, and the whole thing, battery and charger and container and wiring all included, is 9 pounds.