One would expect that the markings M+S or Mud and Snow on a tire would mean that it was designed for proper winter traction in all conditions. You might be surprised to find that it only defines a tire whose treads:
It says nothing about the tire's rubber compound and it's ability to stick to compact snow and ice. In fact, at temperatures below 7 C. it can be expected to perform just like a summer tire in these conditions.
If you are like most tire buyers, my guess is that you choose an all season tire based on the manufacturer's mileage durability claims. This means a rubber compound that stays hard and does a poorer job of sticking to compact snow and ice.
Tires with the mountain and snowflake design are rated for their ability to provide traction in winter conditions where the temperature is below 7 C. Think of them as low temperature tires and choose them over all season tires when you drive on BC's winter road environment.