Cedar City has relatively minor winters and we can usually build all year long. Building in the winter can be slightly more expensive since the home needs to be heated during construction to ensure the drywall texture and paint cures without freezing. And when pouring concrete, we must use special thermal blankets to cover the concrete until it cures.
Another disadvantage to winter building is mud. Often, site access and movement is severely restricted during freeze/thaw events. And, workers will be little slower since everybody is wearing coats & gloves, so they are less dexterous. But these are all manageable, and if you need to be in your home by early spring, working through winter may be your only option. Be sure to discuss with your builder how they respond to winter and understand any added costs associated with winter weather.