How long is your commute? On roads? Will there be real wind? I ask because a mountain bike can be a lot more work to ride distance or into the wind than a well chosen road bike. Dropped handlebars will make leaning forward enough to lessen the effects of a winter wind a real blessing. (That bent over position isn't just better going against the wind; it also lessens the effects of crosswinds on steering.) A road bike will also give you many more options for good tires on pavement.
Having a ride that is less work and more pleasant to ride will make your commute a lot more fun. There are commutes where mountain bikes are better. I am not trying to bad mouth them. But if your commute is paved and longer than maybe 5 miles, a road bike will probably serve you better.
Ben