Why would our kitchen faucet hot water stops working intermittently when it gets cold outside?
Hot water line is closer to the (substitute "source of cold" for "outside wall" in my comment) than the cold water line, and freezes first.

Mysterious water stoppages in cold weather are nearly always from pipes freezing.

The fact that it's the hot water line does not mean that it's full of hot water - after it's sat for a few hours, it's cold, and if it's sat for a few hours by something really, really cold, it will freeze.

Some plumbers can be quite oblivious about this - I've seen pipes clamped to the inside of the sheathing and all the insulation being put on over them - I've also seen those supply pipes, which I was assured would never freeze when I pointed it out, relocated to coming up through the floor inside the wall after a cold spell (not my house, someone else was "in charge" and it evidently took the pipes actually freezing before they would do the job correctly. It probably cost 3 times as much to do over as it would have to do right in the first place.)