Not sure on the legal position but I think the benefits of winter tyres/snow socks/ chains are all subtly different:
Snow snocks – get you moving on snow covered roads, not so much ice. Will have limited braking and steering control as just fabric that isn’t mechanically attached to the tyre. So may be compromised when coming down mountain in icy conditions. Will shred quite quickly if driven on exposed tarmac
Chains – get you moving on snow and ice covered roads. Will give braking and cornering control and are best/safest solution to get you up/down mountain in poor conditions. Have to be fitted/removed as soon as there’s a transition snow-tarmac
Winter tyres – softer compound and sipes are beneficial in all conditions under 7C. Give good ability to get moving in snow and to a lesser degree ice. Give good steering and braking control in snow and to a lesser degree ice.
I’m driving to the alps for the third time in 4 years this feb and have winter tyres (which I like for my winter cotswold commute anyway so no greater cost over the life of 2 x sets of tyres) plus some easy to fit chains (snap onto a wheel nut fitting) that are yet to be used. I got those second hand bargain price so whilst some investment needed it doesn’t have to cost a fortune.