If seasons were on a short cycle, say a few days each (a week, maybe 8 days per "year"), it might not be too bad. The problem would be that, as it stands, you'd HAVE to get on and gather your crop before winter leaving you a small window that not everyone gets to have. (Maybe carrots, onions and such become true biannuals. Harvest for food, or leave growing for seed.)
As it is, with the current season rotation, no, not a good idea.