With my bantams, the SD OEGB, I put a small crate in the back of their coop, and covered it with a comforter for insulation. I sat it all up for them with everything they needed, including deep litter compost. They did very well in that set up. (Other than the fact they were complaining about the smaller space.

) To prove how well that worked, my bantams' waterer was the last waterer to freeze up in a day. (If you're concerned about frostbite, I didn't test this set up for that.)
Something I did with my first bantams, WCBP, I had them in a crate completely surrounded by hay bales, and had hay for flooring. That got them through fine as well, but I don't recommend hay ANYWHERE near chickens. Mine got Red Fowl Mites from the hay, and a BO nearly died from eating some. I'm letting you know about the hay idea, just in case you can figure out a similar idea WITHOUT the hay if you wanted that route.
As far as frostbite, which you're almost guaranteed that on a single combed rooster, many suggest good ventilation, and no drafts. I haven't perfected anything on that area yet, so you'll probably have to ask around for experts.
Your coop might be fine, especially if it's insulated. Going deep litter compost might be your best bet. Remember: Heat rises; and that's one of the few reasons why I like my bantams' perches up high. They'll warm themselves somewhat. (Though again, frostbite could still be a problem if too much condensation builds up.) Compare coop waterers' freeze time to tell you how good it is, or get a thermometer that keeps track of the coldest and warmest points in each of the coops.