The driveline if properly lubed is just fine with winter storage. Likewise the main engine. THe generator the problem is two folks
ONE: it is a carburetor not fuel injection at least not yet. and especially with E-10 they can foul this does not apply to diesels.
This is the major "Engine" issue
There are also electronic parts in the system that need to be "Conditioned" if you let them sit they .. one might say loose muscle tone if one wished to compare to a weightlifter. and then it takes quite a while to build it back up
Regular use keeps it "In shape".
I notice this more with portables When new the waveform even on a quality unit is kind of nasty. but after a tank or two of gas.. much nicer..
On the Contractor models it remains nasty.