When buying new tires it's also very important to check date of manufacture. A tire can look completely new but been on the shelf for 3 years. tires deteriorate/age over time particularly when exposed to direct light. Tire warranty typically expires at 6 years from purchase.
For any sort of performance or classic car, good tires are paramount, you are literally entrusting the car and your safety to the road contact and adhesion of each tire.
I agree you should change your tires and rubber hoses and parts which naturally degrade and rot but to suggest you have to have regular engine maintenance from it just sitting there (and by sitting i mean starting it from time to time and having proper cleaning but not actually driving) is pretty poor design. You shouldn't have to replace a transmission or mechanical part from lack of use. That is just an expensive form of planned obsolescence
The winter compound will harden and perform worse in freezing temps. The overly soft compound is ok in summer for non agressive driving. If, however, they are 'all season tires', it is time to replace. If you see ANY checking between tread, or on sidewall, it is also time. 6 years is about my cutoff personally, 4 for winters stored out of the sun (for use in winter) and 2 years for r compounds/<200 treadwear tires.
These are all ballpark values I have found by experince, and hersay at the track and on the street. I personally find Blizzak and Nokian to fare best in the winter tire niche. They are both good snow/ice hybrid design now, and often used in rally/rallycross.