North-central Wisconsin here -- I finally decided to go with 4 dedicated winter tires on their own steel wheels. I bought the wheels at a salvage yard for $60 for the set of 4. I'm using Firestone Winterforce tires in the original size that my FWD '93 Legacy L wagon came with, 185/70-14. They are very reasonably priced tires in this size. The snow traction is remarkably good, so much better than any all-season rated tires. Choose a tall & narrow vs. low & wide profile tire for getting through snow, and avoiding pothole damage to your rims.
I live where there are lots of steep hills, and we've already had over 3 feet of snow here this winter with no real thaw. So the side roads have been snow-packed for weeks, with icy spots under the snow and slushy spots where they've salted. There are better-rated ice tires out there, but for deep snow traction, these are rated right up there near the top in the tests by Tirerack. After a recent heavy snow I had a friend who is in law enforcement take it for a drive. His comment after driving was that the tires exceeded his expectations. While I have a set of 4 on my FWD for balanced handling and braking, I can't even imagine how much traction these tires would provide on an AWD vehicle. I put mine on in about mid-November which was about when we had our most recent nighttime temp above freezing, and will change back to the normal wheels & tires in April. These tires make driving in snow fun instead of frustrating. They are noisy on dry pavement -- a small price to pay for the ability to get where I need to go during our long snowy winters. (If you live where ice studs are legal, Winterforce tires are studdable.)
I'm interested in the answer to this problem as I have been having the same thing happen with my '93 Legacy wagon with 139K miles. Warm idle looks to be about 500 rpm and the engine seems to be running a little rough, like while waiting at a stoplight. I also notice the slight surging of the revs maybe to 700rpm. I thought with the extreme cold in the minus teens and 20's I maybe had moisture in my gas or something simple like that related to fuel delivery, unique to severely cold weather. Re: turning on the AC - if you have the heater control set to defrost, that would also cycle the AC compressor wouldn't it, as the defrost setting uses the AC compressor to dry the air inside the car?