My quick beadlock research:
Well, just rolled through the Motor Vehicle Safety Act, with Motor Vehicle Tire Safety Regulations (Federal) and the Traffic Safety Act (Alberta) and didn't come across anything SPECIFICALLY against external beadlocks. However, and it would be how you could get fines, the wheels must be put through a proper testing process. AKA be DOT or CSA approved for highway speeds to be used on any public road. Most of the testing for a wheel seems to be aimed at "bead unseating" which of course is kind of a moot point here.... and the rest is aimed at the tire. So that'd be lawyer territory there.
So, if you can find a beadlock with proper weight rating (which isn't a problem unless you drive a tank), is deemed a proper wheel to tire size ratio for diameter and width, and is CSA or DOT approved there's nothing I can see that a cop could possibly give you a ticket for. Unless Calgary has some specific bylaw concerning them.
I also agree with Bill about beadlocks. I've seen a few sets of Walker Evans, and even a set of internal Stauns on the trail all running around 5-7 PSI. None of them had any issue tearing through mud, and they weren't all on M/T's either. I personally like the idea of internals more just because they'll balance a bit easier, and are lower maintenance. But externals tend to be bullet-proof.
I love my BFG KM2's. Only got stuck once since slapping them on. Not sure if that's because they work that much better or because they're 35x12.5' vs my old stock 30x8's and it's just that much more surface area and lift. They shed mud well, nice side lugs, awesome on the road (use them on the DD).