I only have a slow drip on all hot water sides of house. Outside temp is about 2 degrees. All pipes are copper and located on inside walls. I have verified that pilot light is on to hot water heater. I have also verified that it is cycling on and off. What could it be?

Have you recently shut off any outside spigots? Is it possible you shut off the cold water supply to your water heater without knowing it?

Sounds to me like your outlet side of your hot water heater (the HOT side)might be clogged with a mineral buildup(this is especially common in homes with very hard water and tankless coils.

I have the same problem. No pressure at all for the hot water in the kitchen but the cold water is fine. All other faucets throughout the house are fine for both hot and water. What could it be?

What's the outside temperature. Sounds like hot water supply to kitchen is frozen. Lines probably in exterior wall. Hot will freeze before cold. Open cabinet door so heat can get to exterior wall. Provide additional heat if possible. Hope pipe has not busted.