Winter tyres can be used all year round.
Summer tyres are OK for HOT summers
Winter tyres can be used all year round but they will wear out in absolutely no time in warm weather.
However summer tyres wear a lot in winter, so if you run two sets of tyres you'll get more than twice the mileage from them.
Personally I would not bother with narrower tyres because whilst that might help in deep soft snow, that's only a few days a year, whereas winter tyres help a lot on cold tarmac, black ice, mud, rain etc etc and for those I would think width would help.
Nokian winter tyres are probably the best for us as they are designed for snow but also rain, mud and slush in warmer climates with variable winter conditions. Also they are scilica compound (as are many other decent brands I think) which means they should last ages. Having done a winter on mine I think they are probably going to expire due to age rather than tread wear which would be 5 years or so. I drove to Germany, all round the Alps for 3 months and then back, and they still look new.
To answer the OP I haven't got spare wheels because they weren't cheap when I looked, but I will probably get some eventually. It'll help storing them because you are only supposed to stack uninflated tyres four high.
The only reason to replace wheels as well is to protect your summer wheels really.
I would say the main reason is convenience. You don't have to take it to the garage to get them changed over, you can do it in your drive.