BC's designated-route winter-tire rules run October 1 to April 30 (some lower-mainland routes that don't cross mountain passes end March 31). On signed highways, passenger vehicles must run designated winter tires or carry chains.
To be legal, a tire must carry the 3-peaked mountain/snowflake symbol or the M+S marking, be in good condition, and have at least 3.5 mm of tread. The province recommends mountain/snowflake tires for the best snow and ice traction; driving signed routes without compliant tires can mean being turned away and fined.
Vancouver sits in the coastal lower mainland — lots of rain, occasional snow — but anyone heading to the Coquihalla, Highway 3, the Interior or the ski hills crosses designated routes and must comply. That drives a real swap rush in late September and October, so booking early (and using a shop that stores your off-season set) saves a lot of hassle. Most of Vancouver's genuine independents sit on the East Side and along the Marine Drive corridor where lots are bigger; Kitsilano shops are tighter on street parking, so call ahead about drop-off.