Many years ago I was in your situation. As a Canadian studying in the US, I did get accepted to graduate school in Canada (at a top-3 Canadian university). I also was offered full financial aid (no loans needed) for the top-3 Canadian school where I applied.
Of course each case will depend upon specific circumstances, such as grades, where you are, and where you apply. Medical school and veterinary school might be more difficult than other graduate programs.
One nit: If you want to work in Canada, and you are a Canadian who is currently an undergraduate in the US, then there is probably a significant advantage to do your graduate work in Canada rather than in the US.