What advice does the hotel give?

Cars in the winter in Alaska are usually quite cheap. Make a reservation and then check the price every few days (or better yet, submit for price tracking at AutoSlash). Working the rental counter in ANC, it was not uncommon to see rates in the single digits per day in winter. Of course, that excludes coverage, which may be an issue for you (seeing as you're not from the States).

Yes, I grew up in Alaska, but I really don't think you need to worry about the weather. If it does snow, the Seward Highway is the first thing they plow, and the heavy traffic on that road (even in winter) means that any accumulation is very quickly worn off the road, so you're basically driving on bare pavement regardless. Snow is actually relatively easy to drive on; it's ice that is problematic, and ice is basically a non-issue that time of year (because it never gets warm enough for the snow to melt and refreeze into ice). Driving in Alaska is really actually not a thing to worry about. (Heck, I spent 17 years in Alaska and by far the scariest driving I've ever done was during an ice storm in Dallas.) Just keep your distance from the car in front of you, brake early and lightly, be gentle with the accelerator, and keep your speed down so that you don't have to make sharp turns or other quick reactions. When you first get the car, go find an empty parking lot and spend 20 minutes learning how the car reacts on slippery surfaces--gun the gas pedal, slam on the brakes, turn the wheel sharply, etc. and you'll start to get a feel for where the limits of traction are after 15-20 minutes or so. You'll find it's probably better than you think, and then just stay well inside those limits when driving around. You'll do fine.

In the 10 years I ran a rental office in Anchorage (which equates to hundreds of thousands of transactions), I don’t recall a single instance of major damage that was directly caused by a warm-weather renter driving in winter—maybe a dented bumper here and there, but not (that I was aware of, at least) significant damage and certainly never any injury or loss of life. The risk of anything happening is actually very statistically minimal. I wouldn’t worry about it; just use caution and common sense.