There is nothing you can do for the blackened parts of the comb: they are likely dead and will fall off eventually on their own, leaving healthy tissue underneath. I would, however,gently coat the comb with vaseline and/or antibiotic ointment to moisturize the injured areas, guard against infection, and help prevent further damage.
If you can keep the hen inside for a little while, that would be a good idea. I would also make sure your coop has plenty of ventilation (without direct drafts on the birds) and is dry (cleaning out moist droppings can help with this). Beyond that, you could consider adding a safe heat source to the coop, such as a secure, well-wired heat lamp or small space heater kept out of contact with any birds.