They just had the Olympics there. Surely there is a large outdoor venue.
There actually isn't. Vancouver had the first opening ceremonies for the Olympics indoors. BC Place is where both the CFL's BC Lions play and MLS' Vancouver Whitecaps play.
They would have to construct a facility specifically for the game. I'm not saying they wouldn't, but does pose an issue for the Canucks to build a decent facility for one game (maybe two if they can convince the WHL's Vancouver Giants to play). Also, if Bettman is concerned about rain, an outdoor game in Vancouver is probably the worst choice considering a few years ago Vancouver had something like 87 consecutive days with rain in the winter.
I'd suspect you'd see a game in the LA area long before you see a game in Vancouver.
Also, for my money I wouldn't go to a Winter Classic in a winter city. The novelty wore off for me after the first Heritage Classic in Edmonton. I have sat at a football game where it was -40, and that was the Canadian University Championship game. I'm not about to do it for a regular season, largely meaningless, game against the Ducks or whomever.
I still contend that they should figure out how to hold one of these games on the Rideau Canal in Ottawa. But not putting the artificial rink on it, figure out how to make the Canal smooth and play right on the natural ice. That would be an interesting game.
As far as having problems with the ice for a game in LA, I seem to remember LA Live having a skating rink set up around Christmas. I was there in November of 2011 and it was 25 degrees celsius and people were skating. I can't skate, so I didn't test the quality of ice, but I'd imagine it was decent or nobody would skate on it.