You're right, those small prefab coops don't have much ventilation. That's one of the reasons they are NOT recommended by knowledgable folks here on BYC. Don't judge your coop by those. I can't answer as far as snow and ice, we don't get any here except very rarely, but drafts seem to be more of an issue. I'd be more concerned that with chicken wire on the top, predators could get to the chickens.