I live here in the Upstate area too. In the winter they have access to their run always. The only time I keep the door shut in the winter is when the temps get to about 15 degrees and/or winds. They tend to go out till about 15 degrees and that will depend on if it's sunny or not. I just keep an area cleared with a snow shovel and they will make the choice if they venture out or not. I also have a cover on the run so there is not too much snow fall in there.
Hopefully you have some cold hearty birds and they will be just fine.
Hopefully you have some cold hearty birds and they will be just fine.