My goodness! The same advice I got in 1970--deja vu all over again!

That is, some who think it's the wilderness personified and that you need to carry an extra vehicle for the spare parts, and those who say "put fuel in it and go." My 4 times (2 up, 2 down, last one down 40 years ago) were on the old gravel version in Spring, and the secret was keep the speed down. That meant an average of 33 mph for the gravel portion in a motorhome; it's 3300 miles from Cheyenne to Anchorage or vice versa, so it took awhile. Even now that it's paved, I'd say keep the speed down--it's not exactly an Interstate.
My choice is to drive in the daylight, and the days are short in the winter, so I suspect you'll be in the dark a lot more than we were. It cost us one windshield, no tires, no other damage of note--and remember that was on gravel, 4 trips. The only prep I did to the motorhome was to put gravel guards over the headlights. I had several friends who drove it in the winter (made it smoother), and their advice was as you've heard, stay warm--proper clothing, boots, gloves, that sort of thing. A block heater was essential; the rest of the stuff is just good winter planning. There's plenty of fuel along the way, with "road houses" every 25-30 miles, but fuel was/is expensive, as were/are parts and tires. But if you take it easy, the chance of you needing anything but fuel is slim. Our tanks held 43 gallons total, 25 in the main and 18 in the aux, and we also carried 10 gallons in 2 Jerry cans but never needed them. At 8-10 mpg, we never felt short of fuel, normally refilling at the next available stop after switching tanks from the main to the aux.
It's a beautiful drive, so the best advice I could give is to do as much in the daylight as you can--it's a shame to miss so much beauty in the guise of "I've got to get from A to B." Like flying, a good chunk of the trip is the joy of the journey. The hot springs, sure--definitely worth a stop But don't forget to look at the scenery--the deep blue of Kulane Lake, the stark white of glaciers, and on and on. Truly tremendous.
I have friends in Eagle River, too. It's a nice "bedroom community" for Anchorage, without the hustle and bustle of the big city but within an easy drive.
Cary