Yes, you generally can. The availability of hot water depends on the type of your water heater. If it is a traditional tank-style heater powered by gas or propane, you might still have hot water for a while even if the power is out.
What if I have an electric water heater?
In case of an electric water heater, it can't heat water without electricity. Therefore, you might only be able to take a cold shower. However, you'll still have access to cold water as long as the supply is not compromised.
What if the power outage lasts for a long time?
If the power outage is prolonged, preserving the available hot water you have would be a smart move. It is also recommended to have a supply of stored water for hygiene purposes in such cases.