I keep some of my dad's shop towels in the barn. I have NEVER seen anything more absorbent; I need to figure out where he gets them.
But yes, get some towels and DRY THEM OFF. I use my hairdryer at horse shows when my horse gets wet. (If its really freezing I brush with hot water over the dirty spots an then blowdry and cover until our turn to make a run)
No, it is NOT okay to have a horse wet in this weather. And if you blanket them, KEEP THEM BLANKETED. If you pull a blanket off after a period of time the hair is laid down and providing almost no insolation. Since it is your fault their cold, bring the in the dang house if you have to. (Not trying to guilt trip, but this is very serious. I once had a horse get hypothermia because the owner put her out in negative temperatures SOAKED in sweat and rain and the mare almost died)
This may be a bit of a ramble. I didn't really think before I typed this, I just typed whatever came to my mind. But in a nutshell:
1) DRY and get them WARM.
2) Seriously check your blankets...make sure you get some THICK, WATERPROOF ones.
3) Remember this lesson for next time!
I use the Tough-1 Blankets. Not too expensive and I haven't had too any of them rip, although with my rambunctious baby horses, rips are inevitable.
Tough-1 1200 Denier Turnout Blanket - Horse.com
Tough-1 420 Denier Turnout Sheet - Horse.com
P.S.~ I give my horses Omolene and Trifecta with alfalfa in the winter to help keep their body temp up and joints fluid.