As Michelle says, snow and ice are certainly possible at that time of year at high elevations.
Hard to precisely say as every year is different but the end of October is getting later into fall. In most years if you happen to get a snow fall at that time of year, it is cleared pretty quick and the roads are usually rideable relatively shortly thereafter. You have the added benefit of working there and not just travelling though and thus if it does happen to snow, you can wait a couple of days and then head off.
In regards to routes, the google map one you show is the most scenic and you spend the most time in the mountains and I would take that one if it is dry and not too much snow. If it looks like a wet fall and snow is a concern, then I would hop across the Crowsnest Pass into Alberta where you are on the east side of the Rockies where it is drier. Not as scenic as you are on the Prairies but most days it's a windswept road and you would have a straight shot to Grande Prairie through Calgary and Edmonton for example.
So in short, you should be fine if you are willing to wait out bad weather. You have a scenic mountain route if the weather cooperates and a bail out route if winter comes early. If worse comes to worse, I'm 250km west of Cranbrook in Nelson and you can store your bike at my place until spring.
If you are over here in the next little bit, there is some great riding to be had and the weather is still co-operating. I was up at a couple of passes at 1,500 meters biking this weekend, no sign of snow yet although a bit of bite in the air. Drop me a line when you get there and we can catch for a
and some riding.