The above is a misunderstanding of the extent of the reciprocal agreement between CAEA and AEA. If you are a member of CAEA, your union will help you secure the appropriate work permit (in this case, a P2) if you are hired under AEA's jurisdiction. The green card (or an O-1 visa) is not necessary.
From CAEA's website:
"Actors' Equity Association in the United States (AEA) and Equity established a Reciprocal Agreement upon our amicable separation in 1976, which pledges cooperation in matters of common interest, and free interchange of members across the border, including helping members to get the appropriate work permits from the government. The agreement protects each association's members against possible undercutting that could be potentially be caused by visiting artists. Under US Public Law 102-232, you are allowed to enter the United States to look for work within American Equity’s jurisdiction, thanks to our reciprocal agreement. Once you have been offered a job, you must apply for a P-2 Visa: write or call AEA, inform them of your intention to apply for the aforementioned P-2, and request that they send a letter to your engager. The engager must then provide the immigration office with your name, and the name and dates of the production."
Cadence, I would recommend that you begin thinking about pursuing theatre in post-secondary education. Yes, you may be able to get work in the United States on your student visa either in your summers off or in the year post-graduation as MemberName2 mentions, but it will likely not be enough work at a high enough caliber for the US gov't to want to grant you an artist visa (O-1) or a green card. Having been a Canadian who had aspirations very similar to yours, who went to the US to get a degree in musical theatre (I don't regret my choice at all), I was fortunate enough to work a LOT between years and then booked a very substantial non-equity job shortly before graduation. I then had to return home when my work authorization expired. It was a hard adjustment, having spent so much time in the US, moving to Toronto where my connections to big US theatres and theatremakers mattered little. It was a little like starting over, and the people my age who had gone to Canadian theatre schools had a leg up on me when I arrived in Toronto. Keep that in mind. Like I said, I don't regret my choice to go to school in the US--I got a lot of opportunities I wouldn't have had access to otherwise--but just know that there are also fantastic post-secondary insititutions (some are colleges, some are universities, some confer degrees and others do not) to train in MT all across Canada as well. In BC, there's Capilano, in Alberta, there's MacEwan, in Nova Scotia, there's Dalhousie, in Ontario, there's Sheridan, Queen's, St. Clair, St. Lawrence, and Randolph. I've had friends and colleagues go through each of these programs and they've all emerged successful, well-rounded artists, which proves that you really can "make it" coming from anywhere. If you're interested in going to college/university for Musical Theatre, I would recommend you start reading the Musical Theatre subforum on College Confidential now. It's going to be far more helpful to you than these boards. Getting into school for MT is very difficult; by and large, it is harder than getting into Harvard. Preparation is essential and you can never start too soon, as the process gets more and more competitive every year.
Where are you from? You don't have to give any personal details, a province would suffice. Most provinces have theatre networks (e.g. Theatre Ontario, Theatre Alberta) that provide support and oversight for the theatrical ecology within that province. Many of those organizations also provide training (or scholarships for training) for young people who are residents of that province. Let us know where you're from and I can try and dig up some opportunities for you. I used to think I lived in an "irrelevant city," too, but now I realize there were so many opportunities that I missed growing up, and that there are even more now!