What I can say is that it may depend on which Pirelli Winter Sottozero you have: the older Serie-II or newer S3.
The S3 (which I have on my M235i) look like this:
The Serie-II has a very different, asymmetric tread pattern (sorry, no photo') which is much less 'chunky' than the S3. The Serie-II trades-off some snow performance for better dry tarmac handling.
I disclaim any liability for advice, but I'd say that if you have the S3 then it's really not a good track tyre. If you have the Serie-II the dry performance should be better and it should wear less. But that doesn't necessarily mean you want to stress it on a dry competition track.