The reason the mice have come inside is the change in weather, and they're looking for a warm place to spend the winter. Food will keep them there.
If sealing off their entry points is not an option (and they will climb up foundations to find holes under the siding. I've seen them do it,) poison (and I recommend DeCon) or a cat are really your best options. If you decide for poison and the cat, make sure the cat can't get into the poison. You need to move quickly, as they can multiply amazingly fast. I would advise sealing as many entry points as you can find anyway, whatever you decide. Why keep it easy for the mice to get in?
A terrier might be an option, as some of them were bred to hunt rats, but in my experience cats are better mousers.
Lifelong cat lover. Brought my first one home at age 3. Mom made me take it back to the neighbors, though.