Do you expect a UHP summer tyre to work in the winter when the temps are under 7C, whether in the dry or the wet/snow? I mean, they will work, but not very well. The compound simply isn't designed to work at those temps. Your supersports are obviously a step more extreme than the Goodyears I use (Asymmetric 5), and mine are already noticeably less grippy when the temp dips significantly below 7C, so I can imagine yours could be low on grip when the conditions get cold and wet.
When I moved to Germany and bought my Leon here it came with a set of summers (Goodyear Eagle F1 19" ) and winters (conti wintercontact 17") and I haven't looked back.
I've got masses more grip in the winter compared to on summer tyres. Hill starts? No
problem. It was a revelation driving on snow with winter tyres for the first time. It makes you realise how stupid it is in the UK that everyone wobbles about on summers in snow, even if it is only for a few days (if at all) in the South. If I came back to the UK, I wouldn't even think of going back to running summers all year round, it just isn't safe in those rare situations when you need a good tyre the most.
Something very important that no one talks about: I can keep my nice rims away from the salt and crud that gets sprayed up in the winter. No refurbing because of corrosion necessary!
Having said all that, if you found the Conti contact 6s to be acceptable in wintery conditions, go for it. My experience here tells me that it's totally worth the outlay to have two sets of wheels. On a less sporty car than a
Cupra, I'd probably go for a summer-biased all-season tyre like the Michelin Crossclimate, but for my circumstances, I want to take advantage of the German autobahns an country roads around the 'Ring in the summer, so I'll be putting my summer tyres back on around Easter...