yes, they will be fine without a coat as long as they have a nice barn to get into. One year we had over 3 ft of snow and temps got down to -20 at night (a record low) and all of mine did fine, even had some 2 week old Boer kids outside and they were all nice a cozy in their little dog house. Hay is the best thing you can give a goat in the winter, keeps their fire (rumen) stoked. 2nd cut hay is usually better than first cut because it is less stemmy, 3rd cut is better yet and 4th cut is really nice, almost all leaves and very little stems. If you are worried about the hay being too rich, you can take a sample and have it tested.
In the winter I do close up most of the front of my barn, just leave about a 3 ft walk way in each bay so that they have something to get behind no matter what direction the wind is coming from.