Good question. I get frozen dish detergent, if I leave it out on the counter and even in the cabinet under the sink which faces an outside wall. That's because I heat with wood and the fireplace faces the opposite direction from the kitchen.
We finally got a new welder in town and I could get my fireplace insert fixed, so, now my night fires last all night and I haven't had to deal with frozen dish detergent at all this year.