I was just at a similar cabin/snowboarding weekend in Austria a few weeks ago, and it was a blast. The advice from the guy above is good, focus on being yourself and just having fun. In fact, it might be helpful to focus on the snowboarding and drinking aspects of the trip, and let the outcome of the "setup" come as it may; that's the best way to avoid any anxiety and demonstrate yourself to the chiquita in the best possible light. If you're a decent snowboarder, stick near her on the slopes and build up kino/rapport there, which will make it much easier once you bounce back to the cabin.
As for games, coming up with things on the spot is cool, but it doesn't hurt to have some games rehearsed. At our weekend, another guy with us was the one who came armed with all the games, and he was the life of the party by default. Just look up party/drinking games on the web and memorize the rules for 4 or 5 of them that you think the group would be into. Even if it's not a drinking game, it's easy to incorporate drinking into anything

One of the popular ones for us was a kind of "Who am I?" game where everyone writes the name of a celeb on a post-it note and sticks it on someone else's forehead. You go around in a circle with everyone asking yes/no questions about who they are. Every time someone guessed who their celebrity was, whoever was left had to take a shot (or a healthy swig). Good fun, especially with 10 people
The height advice from above is also spot on - don't mention it, and don't let it affect your thinking. Obviously, your friends considered it enough of a non-issue that they're still hooking you up, so why the hell should you care? If you're still stuck on it, there is plenty of good advice for getting around height anxiety and cockblockers on the forum that can help you out, but remember, YOU are the one being hooked up here, so just be cool and enjoy what should be a great time regardless of the outcome.