Okay so I live near Gatwick so it got cold-ish during winter and we had the occasional snow shower. At times it was a few inches deep but obviously not as much as up north. I live on a hill where we get more snow settling than surrounding areas and most people (likely due to them being scared), don't attempt to go down or up the hill when it's snowed.
I used to run MPSS (a predecessor to the current Michelin Pilot sport 4s and 5) all year round and they could handle everything well. However when I decided to get a second set of alloys (£250 for the standard non rays) to run Michelin pilot alpin tyres in the winter (when temps drop below 7c) the performance was transformed during the winter and when it snowed. The grip was outstanding in cold dry a d cold wet weather. It felt like I was driving in the MPSS in the dry.
This one time at band camp... When it really snowed down here and a few inches settled, I was easily able to overtake Range Rovers having issues in their summer tyres.
If performance all the time is for you, get 2 sets. One summer and one winter. Definitely worth it.
If not then I'd say just get a good set of high performance summer tyres like the Michelin pilot sports. Most people aren't lunatics like me and wanting to push their car all year round especially when it's pouring down with heavy rain.