Just because you train in Canada, you don't necessarily get a visa, but these things change regularly - Canada currently is encouraging immigrants - whether pilot is on the list you will have to check.
You mention Winnipeg - you could also try Harv's Air in Steinbach, just down the road. If you get a Canadian licence you can gat an FAA one as well with a small transition exam. You can do it the other way round as well. Neither of them get you any special privileges with EASA.
If you don't need an EASA licence, don't do it.