Well you've kinda got the gist of it, yes it is indeed true that tyre application for passenger cars follows the same rules, that's why there are winter, all-season and summer tyres available!
Tyre grip is directly related to the hysteresis of the rubber compound and this follows a typical curve where, at the lower temperatures the grip is considered unacceptable and it rises to a point of acceptability then on to peek where it is maximum then is begins to fall until it is again out of the range of acceptability.
The acceptable temperature range is engineered by the rubber compound designers and is different for different tyres as well as different for the various season's application.
A particular tyre manufacturer will have their own ideas about what compromises they make during the tyre's production.
Tyre rubber is a visco-elastic material so it does not follow 'normal' rules of friction and load.
If you really want to know about tyre theory there is a super publication released by the Michelin tyre company. It has been around for a number of years in a few different versions. It is available to download but be prepared to do some math for full understanding. However, it is good because it gives explanations also for the lay person so doesn't need to be considered only as technical treatise. I don't have a link for it at present but if I come across it I'll let you know.
Meanwhile, here's a little puzzler for you: when you're travelling down the road at 50mph on your Spyder, the top of your tyre is travelling at 100mph and the bottom is standing still at 0mph.