Woohoo, a fellow Alaskan! I'll have all kinds of tips for you come next winter.
My two Yorkies love the snow. Of course, we don't quite get as cold as you!
As for food, it sounds to me like you're overfeeding, and I don't think cooked meat and chicken is a good idea. Even people who feed meat will tell you that meat loses most of its nutrients when cooked. That's why there's been a lot of interest lately in raw diets.
My personal preference is a high-quality kibble. Yorkies don't eat much, so you can buy one of the higher-end foods at a specialty store (say no to grocery store kibble) without it costing an arm and a leg. There are a lot of subpar dog foods out there, including the Science Diet your vet is likely to recommend.
I'm currently feeding Orijen. It's a grain-free kibble that has gotten real good ratings. If you poke around the health and nutrition forum here, you'll see lots of other suggestions. Here's a good place to start:
http://www.yorkietalk.com/forums/yor...ing-chart.html
As for how much, I feed my 10-pounder about 1/4 cup twice a day. He also gets some extra calories from treats, specifically Yummy Chummies that you can buy up here. I break them into tiny pieces and use them as a reward for tricks, etc.
I'm told it takes 12 hours for a dog to fully digest its food, so many people recommend two feedings a day.
Since all dogs are different, be sure to weigh yours regularly. If he's gaining, cut back on the portions. If he's losing, increase.
Good luck! And keep in touch! You're the first YorkieTalker I've met from Fairbanks.