There are too many variables not to at least investigate finding a rental SUV with AT tires especially if it has a snow flake emblem on it. If the Corolla has to carry much of a load, in very deep snow it will be useless with it’s low clearance. Snow tires aren’t magic, though they are preferable to all seasons on the same vehicle. I have had AT tires that were every bit as good as the snow tires on another 4wd. And, for mountainous potential snow driving, NOTHING beats Awd/4wd with tires with good snow traction. In mountains, Awd aids handling when driving up hills. With fwd, even with snow tires, in dealing with hills you have to drive too fast just to make a hill. Slow and steady is the advantage of 4wd with good traction tres. In parks that require chains for snow with2wd , 4wd vehicles with good tread AT ( not necessarily snow tires) are often exempt. As cold as it’s going to be, I don’t want to be stuck.