Yes, snow tyres are what you need for snow, chains are rarely if ever needed. This is based on a fair number of years experience in the french alps driving front wheeled cars and vans on all sorts of deep snow and ice.
Yes, here in Sweden everybody has winter tyres and I don't think I ever seen chains in use.
About RWD/FWD/4WD. Until not many years ago, most Swedish farmers used RWD Volvos, they live out in the wilderness and didn't seem to have any problems.
The best winter cars I've used has all been RWD, dads old Lada, an even older VW and my own first gen Merc C-klass. With them anyone could be a pretend rally driver round the corners. Even my mum drifted around the corners in the Lada, 'It's easier, you don't have to turn the steering wheel as much'.
The bad ones has all been FWD's. An Honda ATR was worst, with an LSD in the winter booth wheels just spun when you applied the throttle. Older SAAB's with the handbrake on the front wheels (how did they think?).
The other winter the neighbour with an 4WD tried to get up a not very steep slope. Result? Spinning with all 4 wheels and getting nowhere. Never had a 4WD myself, so I'm not the expert.