Small leak at the top of the water heater. It is right at the base of the hot water pipe. The weather has been cold, and around noon the day before, there was no water coming from the hot side of all the faucets.

Unlikely that hot water pipe froze that close to the heater.
Cut pipe, unscrew pipe from heater, coat threads with Teflon tape (at least 4 wraps). I prefer pipe dope (pipe thread joint compound). Screw pipe back into water heater.
If you have heat trap nipples this would be a good time to replace.
Reconnect pipe with coupling (assuming you have copper pipe). If you don't solder, reconnect pipe with Sharkbite coupling.

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there was no water coming from the hot side of all the faucets

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Sounds like the cold water feed to the heater froze up and then thought out.
Waterpipe is leaking? The threaded copper adapter going into the heater? Or is it a brass nipple? Let me know. Back to you, Tom