You should probably, first and foremost, properly research the exact visa requirements for those two countries. I’m not sure about Canada, but for the States, it’s not so much a case of having a degree “making it easier”, but more a case of a degree (I think a Bachelor is actually sufficient but don’t take my word for it) actually being one of the requirements for an H1B visa. There are other requirements too, but probably the hardest part of that process is securing a job offer, which is also a requirement for a visa. And considering you’d be applying for jobs in a country that already has a surplus of experienced local artists, that’s no easy task.
In addition to that, if I recall correctly, I think your degree has to be related to the field you intend to work in. Whether or not the argument can be made that your existing degree could be put to use in animation is something that a US immigration attorney would be better qualified to answer than myself. So there’s definitely some important research required here before you make your education decisions, as you may actually need to do a degree in something art related, but again I must stress that this is something you should investigate with someone educated in immigration law.
You don’t say where you’re actually from, but the most realistic course of action you could take would be to work for several years locally after graduating first, beefing up your CV with professional experience while developing your skills on production work. As I said earlier, the chances of being picked up by a US or Canadian studio as an inexperienced junior artist from abroad are virtually zero. You’ve certainly picked a tough goal, so I hope you understand it’s likely to take many years to achieve.
