I used to take a big old wool blanket from in the house and put it over them. It'd go up their neck like a cooler but didnt have straps so I just bunched the fabric under the horses neck and clipped it or tied it with a hair tie.
I've used regular fleece blankets, and an old quilt over that if needed if it was really cold...then just walked him until he was cool and tied him up while I did barn chores, and took blankets off when he was dry, and refluffed.
I used to use towels to help dry my friend's horse off. It worked well, just let him be in his stall until i'm done putting the tack away and getting his food ready seemed to be enough time for the remainder dry off. (he sweats a lot, almost every ride no matter the weather or amount of riding)