Hi there: we live over at Anglemont in B.C., so our climate is very similar to yours. I will say that there are a number of tire retaining walls in this area, and by the looks of them, they have been here for a number of years.
In order to avoid the potential problem of your tires "floating" which I don't think they should do, may I suggest you try this.
First dig about a foot below grade where you need to place your tire wall. Put about 6" of sharp rock in the trench. Use a tamper to pack the sharp rock really well. Add your first row of tires and pack it hard with dirt, I don't think you need to use expensive stones, but if you have fist sized rocks by all means use them. Fill behind the tires with at least 6" of sharp rock again. Repeat until your tire retaining wall is at the height you desire.
We did a retaining wall last year, but out of concrete blocks. Honestly, it was way too expensive. But we used the method above, using the sharp rock to provide adequate drainage behind the wall. We did use a tamper to pack the stone hard between layers, and I'm told that is a critical step.
We have just gone through a terrible winter, very cold, lots of snow and now lots of rain. I know our relatives in Calgary are complaining about the SNOW today! It has been a strange one.
Our wall - so far - is still just as we built it. So it appears the system works.