Water is froze does it hurt to leave hot water heater on ?

If you don't leave it on.....then drain it. Cracked tank due to frozen water is lot more hassle & $$$ then leaving it on.

Can't hurt because water can not be fully used out of tank so there will always be enough water in tank to absorb heat from running it.....just like the WH at home. Sits there heating as needed even when no water demand has occurred.