No where in BC is it mandatory to have chains on your personal vehicle while crossing the mountains. Although there are very big signs that tell you "Severe winter conditions, winter tires and chains required" but you can still go, no one there to say otherwise.
Now commercial vehicles..which I drive...If the chain up light is on, you chain up!! If you don't and spin out on the hill you can be fined several thousand dollars, plus a $400-800 tow bill etc.
I know in Sweden you have to have properly rated winter tires. If you try and cross into Sweden from Denmark, or Norway, they will deny you entry and turn you around if your tires are not up to spec.