You can absolutely wash her legs, especially from the knee down, even in cold weather, especially if you can towel her off well afterwards. We wash in colder weather (not because we want to - my gelding has struggled with very loose stool this winter, and has needed his hocks washed frequently so we do it anytime it is near or above freezing), and I live in Eastern Canada. If you don't have access to warm water in the barn (it doesn't need to be hot, just warm), heat a little up in an electric kettle and add cold water. If they don't like you using an electric kettle in the barn, you can also bring hot water in a Thermos (but you'll likely need several).
Have lots of water on hand so you can rinse thoroughly. We keep some of those dish gloves that nearly go up to your elbows for this purpose :) and have buckets just for washing. Also, a few small rags/hand towels you can pop into a plastic bag for washing afterwards. A thorough drying will keep her from getting cold. A little walk afterwards helps too.