After an extended power outage during a winter storm, your heat pump refrigerant will be sluggish when the power finally returns. To avoid damage, you should run your unit on supplementary (or emergency) heat for the first few hours. Not doing so could damage your heat pump.
Also note that in older neighborhoods, the sudden demand for electric power might cause power quality issues that might also damage your heat pump.
If your home is equipped with an electric heat pump, special care is needed when turning the unit on after an extended outage. It takes a period of time for the lubricant in the refrigerant to warm-up. This is approximately one and one-half hours per ton of cooling capacity. This could vary from brand to brand and a call to your dealer could prevent problems. During this compressor warm up time you should use the supplemental or emergency resistance heating elements of the heat pump to heat the home.