I feel your pain, I hate dealing with hot horses in winter (in summer no issue as just shower or sponge them off and leave in the sun to dry). Is your horse clipped or unclipped? Mine are unclipped as turned out un-rugged so have lovely thick fluffy winter coats which does have the side effect that they get very sweaty very easily. The first thing I do is be a bit cognisant that it's an issue at this time of year so I am careful to not do too much fast or intense work to avoid them getting overheated in the first place, and then I am very careful about gradually cooling down at the end of the ride, so we go from proper work to gentle stretching in trot and then walk for at least 5-10 mins, then I usually hand walk for at least 5 mins after riding with the saddle off, this does a lot in itself to cool and dry them. If still sweaty after this, I wouldn't want any cold water on them, my concern is them getting chilled from being left to stand while hot, which isn't going to be helped by sponging/washing, unless you are lucky enough to have a hot wash and/or solarium facility. So I usually make a wisp (bit old-fashioned, effectively a straw brush, you could use a body brush, I just prefer the wisp as it doesn't take off any of their natural coat oils) and wipe/brush off the worst of the sweat, stick a cooler or fleece on and leave to dry. Once fully dry replace the cooler with whatever they normally wear in the stable. Dried on sweat marks are unsightly but won't hurt the horse so long as they are kept warm and left to dry gradually, and can be easily brushed off when totally dry... OTOH do feel free to wash/sponge off your girth and saddle cloth to your hearts content, as these will have absorbed a lot of the sweat, I can't stand the feel of sticky/sweaty dried on sweat being put back on the horses back so am a bit obsessive about washing everything that goes on them!