I can't tell from the pic how much air can get in from the bottom, looks like it's fairly non-airtight at the bottom, so I'm thinking it should be all right. However, if you just leave the door partially unzipped, as in the pic, all should be good.
Are you planning to turn the pile any during the winter?
Dribbling thoughts: If a structure that size was airtight I wonder how long it would take for your compost pile to completly replace the oxygen with CO2? And then how long would it take before the Anaerobic organisms come alive and fill it up with methane....
I wonder if this is true in most piles about oxygen being used up within 15 minutes ( I guess it depends a lot on how "lumpy" one's pile is): https://www.youtube.com/watch?v=YZpCyMUFeAk&feature=related