When we built my coop last year it is 8x12, 8 foot tall on one long side and ten on the other. When i asked someone who drafts house plans, he said even with the 1/4 drop, I should use 2x8s because of snow load--and that's with a metal roof. It depends on how much snow you get in your area. Most of the time we only get 8-12 inches at a time, if that, but decided it was worth the extra cost to make sure I wouldn't have problems down the road. I would definitely do at least 2x6s if I were you.
Insulating cost us a pretty penny, but my banties stayed much warmer last winter, and are much cooler this summer than the rest of my birds, so it was well worth it.