Getting out of the wind is really helpful for cold weather repairs. Difficult if you have a rural commute, pretty easy for city dwellers. (bus shelter etc.) Have thin gloves that allow for dexterity but some warmth, use a spare tube (deal with patching the flat one indoors later!) Should be on your way before you cool down from being heated from riding.

Although I have not had any flats in really cold weather, maybe a 2-3C december day. (knock on wood now...) And that day I probably would have hopped the subway as my ride was paralleling it except I was headed to a party carrying beer in my pannier and the thought of negotiating the heavy bike + beer down the subway station stairs I opted to just fix and go.