How odd, it's usually cold enough that we don't have problems with ticks in the winter.
I've certainly never seen them on animals or myself, not even in the warmer winters but then again I live in a more open area -no forests.
If your cat is staying inside then there shouldn't be a problem. Stomp your shoes before going in and dust off your pant legs. Remove any outer clothing, such as hats, shoes, and coats in an outer room (screened porch, utility, mud room), and don't run around in heavily wooded areas yourself.