There’s a few things that change when trying to keep your muddy pasture puff clean occasionally in the winter.
To keep the horse comfortable if it’s too cold for a full body bath you can always just wash the mane, tail and legs. Leaving the horses majority of their body dry to keep warm.
If it’s 50-60 degrees out you can full body bath but be sure you don’t bathe later than 1pm so they have time to dry off and don’t wet their belly or wash their belly. That’s the last part to dry off in general and will give them chills if it’s wet when it’s cold out.
Should you use warm water? Yes if you can but sometimes if warm water isn’t available with the hose, I fill up a soapy water bucket with warm water and use it to lather then use the hose to rinse but make it quick.
At the end of the bath cover with a fleece cooler, dry off the horse with a towel and wipe the hair backwards from the normal direction to help aerate the fur for optimal drying.
Keeping the shivering horse warm if they start to feel chilled, make sure they have grass hay to much on. Eating helps them stay warm.
Good luck and be patient, think how you would feel getting an outdoor shower in the winter… a wiggly horse is almost always to be expected.