Here's the secret about snow tyres, or winter tyres, or all-season tyres: Every manufacturer puts out good ones. The difference in performance is not from choosing Brand A vs. Brand B, it's in making sure the tyres are the right size for the car, and the right feel for the driver.
Some tires are more aggressive than others, with deeper tread and larger lugs, and offer a noisier ride on dry pavement but more traction in snow. Other tyres have less pronounced tread, and thus somewhat less traction, but offer a quieter and smoother ride on dry pavement. The choice is personal, and depends on a driver's tolerance for noise, and the amount of on-snow driving done in a winter.
Buy tyres before need for them arises. Discuss options with the tyre dealer. Never mix radials and normal tires.
The RAC advises drivers to check their tires for wear, and to make sure they are properly inflated. Colder temperatures mean a difference in air pressure, which will affect a tyre's performance, and make it wear faster. Drivers should check tyre pressures often, before setting out, when the tyres are cold, especially in autumn and spring when temperatures are changing most dramatically.