Like above is there cold water flow out of the hot tap or no flow at all? if you have an outdoor shower with a sprayer make sure the valves are closed as this can bleed cold into the hot. If no flow I would bet the hot line has frozen, insulation on its own will not stop freezing, it is just a barrier keep the heat from escaping. So if you are relying on just pipe insulation to stop freezing it will delay it but unless you have constant flow you will need a heat source to keep the pipe from freezing in the long term. Also hot water lines can freeze faster than cold water lines.