I think it will work, but I think it's too early -- I'd wait until you have as consistent cold as you are going to have then sow.

I think if you plant now, they will germinate now, and either be killed, or become vernalized and bolt to seed next year.

However, just a hunch, so maybe someone who's done it will come along with a real answer.

I overwintered young carrots last winter. The greens were still alive in the spring but the roots were soft and rotten. But I am in zone 2 with five months of snow cover and you are in BC. I think you have a better chance of success.