I'd love to know how this worked out! I had a friend, once, who grew up in Bulgaria and she told about starting tomato plants in the compost in early spring because it was hot enough to germinate the seeds there. I'm pretty sure they had lots of fresh cow manure to heat up their compost, though, but she told about compost heaps under the snow....
It was years ago and I wish I remembered better some of those details. Anyway, I know from that that there are ways to make it work.
I've been known to save kitchen scraps in the freezer for weeks and even months, until it's warm enough outside to work them into the compost. But I have never lived in an Alaskan winter!