Probably your best bet would be to read through the FAQ section of the Rose Propagation & Exchange Forum. There are differences in types of roses and a significant amount of info to cover. If you still have questions, please ask specifically and we can cover those questions. You might also skim through some of the threads in that forum.

Here is a link that might be useful: Rose Propagation & Exchange Forum FAQ Page

For generally propagating anything, and if/when you're going to cut them anyway, you can stick the pieces (in the same direction they were growing) as deeply as possible in the soil, either where you want new plants, or in a place where you can move them easily when needed.

If any of the branches you intend to cut will bend to the ground without breaking, ground layering also usually works. You would lay a rock or brick on the branch to hold it in contact with the soil (removing any grass or leaves in the way.)

I usually do both of these (for about any kind of plant) in the spring but if you're going to trim now anyway, it would be pretty easy to attempt. Those in a similar climate would be best to advise about the possibility of success over winter of propagating roses in particular with these methods. I've gardened in OH, but that's nowhere near as cold as Canada (most winters!)