Step one if you haven’t is get a spare set of wheels for your winter tires. Most common winter size would be the 185/60R15 mentioned.
Nokian, Bridgestone and Michelin all make great snow tires. Another standout is Continental. General makes decent snow tires as well
Nokian Hakkepelita R5
Bridgestone Blizzak WS90
Continental VikingContact 7
General Altimax Arctic 12
Michelin Ice-X Snow
If you can change your own wheels and reinstall with a torque wrench, many of these are available from Tire Rack pre-mounted on a set of wheels (steel work well for winter), otherwise your local shop can do it, but you’ll save time and money being able to switch them out, as true snow tires are quite soft and wear quickly if they see a lot of dry pavement driving. Some will also feel a bit soft and squirmy on dry pavement.
There do exist “All-weather” tires which are long wearing all-seasons with snow rating, but they are a compromise and are not as good in the snow and especially icy conditions as a real snow tire due to the hard “all season” rubber and also not as good in the dry as an all-season due to the tall squirmy tread blocks
My favorite so far have actually been Continental WinterContact TS870 but they are hard to find in the US and not particularly cheap.