I am having siding put on my house. There is currently very little insulation on the west exterior side of my house. I have hot and cold water supply from the basement on the west walls. My wife complained the hot water was not coming out of the sink, single handle. I could not figure out the problem after taking the faucet apart. Put it back together and the cold worked fine. Toilet next to the sink had water supply and the shower in the same small bathroom functioned fine, hot and cold. This morning no water to any of the fixtures in that bathroom. The rest of the house if fine.
We have had temperatures in the single digits two nights in a row. I have not found any evidence of a broken pipe or leak.
Any thoughts

You usually will not see evidence of a broken, frozen pipe until it thaws. If the pipe broke due to a freze it usually doesn't burst and shoot water all over like you might picture. I think your pipes have frozen and may not have burst, yet. Open the doors under the sink and get some extra heat into that room before they do burst. If the pipes are inside an exterior wall you need to get some good insulation in that wall cavity or consider some type of heat tape.