Car dies in freezing weather, alternator repair related?

I have a Maxima 2000, 138000 miles. During this Midwest below- freezing weather snap, my car has started fine, but has died a couple times about 30 seconds soon after starting. This is usually after I leave my car parked in the parking garage for about 10+ hours. The car starts up again and I don't have another problem with it as I drive home. Of note, my battery and brake lights were flashing last week and I took it into the shop and was told I needed a new alternator, which I had the mechanics replace. My battery and brake lights don't flash anymore, but now my car seems to die as described above. Did the mechanics miss something, or is this all freezing cold related? Any advice is greatly appreciated.