I guess I can probably answer a little more:
I'm a foreigner, from the UK. (pimple faced Brit!!!)
Couple of ways to get in: 1) Sponsorship/LMO process
2) Working holiday program (under 32 years old only)
3) Permanent Residency options.
Currently there is no Working holiday program for US citizens. Unfair? Probably not, as the USA's immigration policy is so ridiculous, I'm almost certain they've burnt bridges with visa for their own citizens elsewhere.
For sponsorship, still possible but not easy. You need to apply a lot, you won't necessarily get a job where you want, but it's a foot in the door. The work permit limits you to where you work (the resort and department) so there's no chance of supplementing your teaching with other jobs. Other issues with the LMO system is as follows:
A) 20 hour work week guaranteed....not bad right, but when times are slow, Canadians aren't working because you need the hours to fulfill your hours...little animosity.
B) Work permit length can vary and change as per required, I was limited one season to only 10 weeks. So I only had 10 weeks as a valid worker, and then had to leave, (I applied for extension as a tourist and was ok to stay)
C) Sponsorship is often only offered to high cert instructors, many hills are looking for CSIA/PSIA 3 or equivalent minimums. - that being said you have dual cert so that will play in your favour.
Finally PR...if you have Canadian family, you can be sponsored by them....