At my stables, we don't bathe them with a horse or anything, but put a washcloth under warm water to relax muscles and make the horse feel warm and fuzzy, and rub it on areas needing to be cleaned. You don't want to use freezing cold or boiling hot water, it can injure or shock your horse. Hope it helped!
I bathe them completely for shows. I dry them with a towel, put two fleece rugs on them, and at work I put them under the solarium. If you only have cold water or no barn where they can dry out of the draft I would just sponge bathe or use spot remover 😊