Depends. How cold did it get? If it was below freezing unprotected for more than 5 hours, it's in trouble for sure. If the core is frozen, it may not make it. I've had some do that too....just keep rotting down, down, down until they were mush. One came back from the very bottom, though, so don't give up completely. On the other hand, if the soil froze, it's toast.

If the ugly stick lives, there will be shoots coming out of the sides, and the top will die down to the first shoot and eventually fall off. Leave it alone if it does that, and do not cut that top dried out part off until it falls off on its own.

I had one die down to the ground once, and I thought it was gone, and suddenly, one shoot came up from just below ground and grew into a beautiful plant.