[Poicephalus girl]

I also live in Canada and I also like keeping my house (well appartment) on the cool side (which is around what you have been mentioning). In the winter, I do put the AC on, but I mostly use it to get rid of the humidity and it's not blasting too much cold air.

The problem is really how sudden the change in temperature might be, aka going for a heated house in the winter to outside in cold weather without proper isolation. If the difference is great, then that could be bad for the bird.
There are stories of cockatoos playing in the snow and being fine; however, they lived out in an aviary and were accustomed to the weather (mind you, this was not in Canada and I don't it got as cold as it does here in the winter and this snow didn't accumulate as much..)