HVAC companies get really busy in the summer when it is hot. They like to get some service work in earyl spring and fall, to keep their crew working when big repair/replacement calls are fewer.
The equipment could care less when you perform maintenance, and a heat pump system requires very little. Coil cleaning is a good idea, and general cleaning and inspection is a good idea. This service should not cost an arm and a leg, and a good company will not be trying to sell you costly repairs every time. Many people do not bother to get the coils cleaned and put anit-legionaires tablets in the condensate pans. These folks get by for a few years, but sooner or later get bit.
To repeat the answer to your specific question: it will be easier and cheaper to find a service company in spring and fall. In the heart of the cooling and heating seasons, everyone is busy, and no one has any time for inspection calls.