There are a lot of good suggestions posted by others.
What has not been mentioned is that that pipe is likely to burst. Generally, it will burst on Christmas or New Years.
This year I bought a house. The pipes to the kitchen were in a wall similar to your configuration. The previous owners managed to keep the water from freezing by deliberately having a drip in the basement. Awful odor.
I couldn't take the odor any more so I turned off the drip when the weather was warm. I missed one cold night and the pipes to the kitchen froze. I got lucky: heating the pipe with a blow torch worked. I don't recommend this.
Fortunately, I've done a kitchen remodel. Even though the new walls are 6-inch framing, I still moved the plumbing inside the house.
A thought occurred to me: You might have a pinhole leak in your exterior sheathing and siding. That could cause your pipe freezing problem. I'd carefully look for nailholes and plug with caulk or foam.
I had a pinhole leak in a former house. The leak was in a crawl space and was a good three feet from the pipe but it was enough to cause the pipe to burst. Ugly mess.
Nonetheless, even though I am not a plumber, I strongly suggest that you deal with the problem before it becomes a PROBLEM. Ripping out a small section of drywall and repainting is a lot cheaper than having a pipe burst and having wet insulation and god-knows-what else (mold?) that you would have to deal with.
Remember, if that pipe bursts in your wall on Christmas, you'll not have water in your entire house and it could ruin your holiday as well as your wallet.
Another thought: Can you insert a shutoff to the toilet at the main level? Maybe you could then turn the water off to the toilet in the winter?