I have a similar commute -- 30 minutes each way, in south central Wisconsin. I'm equipped specifically for my commute: For warm weather I ride a venerable old touring-style bike, and carry rain gear in a bag. For winter, I have an old mountain bike with studded tires. There's a lot of athletic clothing available for winter riding, but I just wear a ski jacket and snow pants. If it gets real cold, like below -10F, then I wear a ski helmet and goggles. I'm lucky that I don't sweat a lot. During the summer, I just start from home earlier than usual, and ride slower, so I don't have to take a shower when I arrive. Some kind of layer system can be helpful, because there are months where the temperature changes by 30 degrees from morning to afternoon.

Granted it takes some space to have more than one bike, but I have a garage. On the other hand, some folks just keep a second pair of wheels with the studded tires. When buying a bike for commuting, it's good to make sure that there's enough clearance for fenders and wider tires if desired.