When I was a kid we lived in St David, ME, and went to school in Madawaska. So I know cold. We had goats, but the kind with upright ears, not Nubians.
The key is to have a draft-free barn, and if you can stand it, let the poop and bedding start building up in fall, just add new stuff on top. It will compost and create some heat, especially if it can get 2-3' deep. Of course, it will compost out your walls, too, so keep that in mind! And will be NOT fun to clean in the spring, unless you have pigs you can put in there for a few days to plow it up for you.
It is essential to have at least two, preferrably several, goats who can sleep together and snuggle, well off the frozen ground. Lots of hay free choice....the fermenting in their digestive tract is what will do the most to keep them warm. And if you can get an electric water bucket, that helps, or at least bring warm water to them at least twice a day so they can drink deeply before it freezes, and not get chilled in the process.
A few years ago I built an insulated bucket by using a muck bucket for the outside, a piece of plywood cut to fit on top with a hole cut in it to accomodate a five gallon pail. I filled the space between with styrofoam packing peanuts and filled the gaps with Great Stuff spray foam insulation. I was going to screw the plywood top to the muck bucket, but the Great Stuff is also great glue, it seems! That pail will rarely freeze if filled with warm water and placed out of drafts. I used it for my horse, but my pygmies couldn't reach it, so now in the winter I do something a little different.
I use a big rubber ground feeder, put some shavings in it, and set a smaller plastic feed pan in that, which I fill with warm water. It stays liquid much longer then just a bucket would.