While ICBC recommends the use of snow tires in snowy conditions, and driving without proper winter tires may not be the safest decision, it does not affect a customer's eligibility to make a claim and it does not void the driver's insurance (although it could lead to ticketing by law enforcement).
In the event of a claim, the act of not having or using the appropriate equipment doesn't automatically mean a driver will be deemed at-fault. However, drivers involved in a crash who were not using snow tires or chains when appropriate may be deemed negligent, and could lose their discount and face higher insurance premiums on their next renewal.