If you put an apron of hardware cloth around the coop, that will help with rodents, digging predators. You can do deep litter on concrete, but if I were doing that, I'd put a thin layer of dirt on the concrete, then the bedding. Until the new coop is up, move stuff around and let the chickens scratch up the tunnels. They love mice.
You can have an open front, as long as that isn't the direction of the prevailing winds. Keeping chickens warm is a matter of stopping drafts and having adequate ventilation. Chickens body temp is about 104 with a warm layer of feathers to keep it in. The vulnerable parts are comb, wattle and feet. If the coop is dry, and there isn't a draft on them, they stay warm. If there is a direct draft or it is wet, then frostbite is more likely.
Check out the Wood's Coop design, that might be what you are looking for.
