Amir said:
I also endorse using tires for snow travel.
What about rocks? 
Rocks are tough to mount and don’t hold air well. 
If you have a long, cold, wet/snowy winter, snow tires are worth it—emergency services use them for a reason. Consider a set of winter tires with inexpensive steel wheels so you can easily swap. Studded tires are great in icy areas but wear quickly on dry pavement and aren’t always allowed.
If snow is rare, good AT tires and chains work too. I use Les Schwab Sport LT chains on my ATs for the Sierra.
I live in New England, never used snow tires. It’s about learning how to drive in snow. I avoid the roads after the first snowfall because everyone else seems to forget snow and ice are slippery!
I use severe snow service-rated ATs year-round because I’m too lazy to swap. Duratracs are my go-to, but Falken Wildpeaks are popular too.
I live at 8500 ft in Colorado and see over 200" of snow each season. For city driving, get dedicated snow tires. Blizzaks wear fast, but Nokians and Michelins are good. Duratracs have the most siping among off-road tires, so they perform best in snow.
If allowed, go with studs for extra grip. I use studded Duratracs for my rural driving needs, often through several feet of snow. During summer, I switch to regular off-road tires.