You wouldn't starve, you'd just have to start lowering your standards as the hours ticked past. That 3-year-old steak in the freezer that you feel guilty about discarding but that you'd never eat by choice? That's going in the microwave. Gross canned soup? Fair game. You probably even have a box of instant oatmeal—God forbid—stowed away somewhere.
Otherwise, the rule of threes (three minutes without oxygen, three days without water, three weeks without food) pretty much precludes any chance of starvation from the kinds of snowstorms we see. Some people were snowed-in for a week after the Lindsay storm, and that was just a spectacular display of political bungling, so it's probably hard to go much longer than that.