Don't worry about washing her...they make some wonderful lice powder that you can buy, that works great! And in cold weather, it's the way to go! I got some at the TSC in town when it happened to me a few years ago, and I had several horses that "shared" in the experience.
First worm her with Ivermectin and powder her coat, working it down to the skin with your fingers -- making sure you get down into and under the mane and the base of the tail. Keep her powdered up every few days, and reworm her in 2 weeks with Ivermectin again. She should be clear after a couple of weeks -- and no bath needed! If you still see any evidence of them, continue with the powder and worming routine and they'll disappear!
Much nicer and less worry then bathing in the cold!