The most economical and versatile way to go, is going to be with a mid sized tractor with a minimum of 35PTO hp, a FEL, and a rear mount PTO snowblower, used.
You can get a good used full sized CUT, or smaller Utility sized tractor, open station, for 15-18k, and cheaper depending on your needs/wants.
Then find a good quality, medium or heavy duty snowblower wide enough to cover your tracks (I'd prefer closer to 40PTO hp on a 6' snowblower based on the massive amount of snow you'll run into). I would certainly go with a good quality used blower over a new lighter duty blower for the same price (even if the used costs more than a light duty new. Something like a Pronovost Puma series is going to be pretty light duty, but if you step up to the Pronovost Group 2 snowblowers, you will be much happier and it will last much longer.
If you got a lot of heavy wet snow, I would recommend something with a rotating shute like the Pronovost P-860TRC blower but that is a bigger, more expensive blower that demands more HP. In your situation, I'd not skimp on the blower, and PTO HP.
After you have those two (hopefully within your $20k budget), I would absolutely, without a doubt, recommend investing approximately $300-$400 dollars into a permanent mount heat controller, electric heated jacket liner, and electric heated gloves, as well as some some good head gear and goggles.
Warm & Safe, the Home of the Warmest Clothing in the Universe This place makes some of the best heated gear out there.
It may seem silly at first, but it makes all the difference in the world. I have been out there with the wind blowing, in bitter cold, and wearing my heated gear with the "Heattroller" wired to my tractor, and have never once been able to keep it on full power. This is my "poor man's cab" until I can save up enough cash to purchase the "rich man's cab".
Just my humble opinion
EDIT: I've had mixed success depending on the "hardness" of the ice, with breaking it up and putting "grooves" in it for traction, by using a "Ratchet Rake" on my front end loader.