@naugeleh all-weather tires (note: different from all-season) these days are really good. if you're not already driving using them, you should

chains are good to have if you're crossing a mountain but are kind of a last resort option i feel

my biggest concern with a prius isn't the lack of all-wheel-drive but the low weight. studded snow tires might actually be a liability in that situation because if the car isn't heavy enough to actually push the studs into the ice, you're just decreasing your surface area + traction. we had this problem with our old civic as i recall

i would get good all-weather tires that maximize surface area for driving in snow and ice, have chains in the back in case you really need to get somewhere, and just drive slow + safe + careful as possible otherwise