I just went thru this.........
My bet is that your kitchen sink water lines are t'eed off the low point drains for both hot and cold. If you look under the sink, remove the mouse blockers if you have them and shine a flashlight down the hole. Chances are you will see ice. The low point drains on my RV are exposed under the RV, and are probably the first thing to freeze in cold weather. I put a small heater in the cupboard and just waited. Sure enough after an hour or so, the hot water worked again.
I have not done it yet, but I will insulate and put some heat tape on them when I can.
It's still a mystery to me that the cold water line which is next to the hot water line did not freeze.
Hope you and yours are dealing well with the deep freeze.