If you rent, you are at the complete dependency on the tires on the rental. But, you may not be stuck with all season tires. IMHO, you just may find a rental Awd with AT tires. All seasons wuld be too big a compromise if they had too many miles which you have no control over. Go over to the lot. Take a tire gauge and your smart phone and check reprorts from Tire Rack or oters on the spot when you look for a car. Otherwise, if you aren’t willing to do that reaserch, stay with the Corolla. But, Awd with decent AT or snow tires are the ultimate choice.
A 4Runner for example, should have them standard.