For 2 miles you could ride shirtless and you'll live. It'd be awful and you'd never do such a thing again, but it's only a 15 minute commute.
I'm going tommorow and it's going to be incredibly cold, but as long as you cover up exposed skin you'll start producing your own heat and be nice and comfortable within 10 minutes provided you've had proper winter clothing all along (ie, proper layering).