I believe out of Anchorage, Dollar, Thrifty, and Budget offer studded tires on a very small selection of their fleet--and standard cars only, no vans or SUVs. They charge around $20 per day for the "upgrade" to studded tires.

Highly doubtful they'll have any studded tires available so early in the season. Studs aren't even legal in Anchorage until September 15, and very few people put studs on that early because the local weather simply doesn't require it until much later (and the more time studs are on, the faster they wear out).

Standard tires on rental cars are always factory OEM all-seasons. They do not put anything special on for the winter (other than the above-mentioned studded tires available for a fee). All-seasons are fine for most normal driving; I never bothered to put studs on the two last cars I owned while I lived up there and never really felt that it compromised anything. But then again, I didn't really ever leave Anchorage in the wintertime. If I did, though, a rental SUV was sufficient for me to feel protected.

(Note that AWD/4WD does not help with stopping, so while a big, heavy SUV often feel safer to drive faster, it really isn't. The AWD/4WD can help you get out of being stuck but doesn't prevent you from sliding off the road in the first place, so keep speeds and following distances down!)