My guess would be late March to april that is when the weather starts to warming up. It has snowed on that highway even in late march, the higher the pass the more likely hood of snow. I would chech the weather report for the Manning park areas before travelling, that would probably give you the best indication of road conditions.
I drive through that area fairly often and, in my experience, you could do the trip anywhere from March onward as long as you go here [below url] first and check ALL the appropriate sites. The radar-sat images via Environment Canada are especially good for such trips.
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