Thanks to the three of you for the comments.
The thrust of your argument though is to imply that summer tyres should be made of a compound closer to that of winter tyres, even if without the deep tread. But summer tyres already are made of what the manufacturers think of as an 'optimised' compound balancing 'softness' with wear.
I did not think that tyres gripped snow as such, but used the deep tread to 'squeeze' through the snow, just like normal tread disperses rain water.
In southern England we rarely get snow and then it is usually a thin layer that melts quickly, especially in London. We do get slush occasionally, for which, of course, deep tread is useful.
Tyre temperatures may well equilibrate at lower temperatures than in summer, but these must be above 7 deg C, at least when ambient is about zero or above. Or have I missed something?
DAS
For direct contact replace nospam with schmetterling