Around Thanksgiving week last year, we had over 20" of snow and I thought to keep my girls locked up, warm and toasty. They went absolutely bonkers!! So I opened it up for them and they went out in it - happily and willingly. Mind you, most didn't stay out for very long, but they had fun and were very happy.
Point is, if they want to go out? Let 'em. They'll decide if and/or when it's too cold for them. If they don't want out? They'll stay in regardless if the door is open.