Adapting to steeper terrain is more difficult. The terrain at big western mountains (squaw, jackson, whistler) is MUCH steeper than anything in the east.
I grew up back east, and the first time I skied out west I was on skinny bump skis. I thought I could ski anything, after icy vermont bump runs, but I was wrong. You will have a huge advantage if you have skis that are at all fat. Even park skis nowadays are about 85 or more under foot, the skis I learned on were 63 or so. Skiing chopped up refrozen crud, or breakable crust is a whole lot more difficult than skiing pow, or east coast hardpack for that matter, but once again we have the advantage of fat skis, which makes learning much easier. Trying to learn to ski deep snow on skinny skis was really tough. It took me several trips west and alot of effort before I found it fun. My first two trips out west I longed for east coast ice and bumps, where I felt like I could ski.
Even on fatter skis, it helps to keep your skis together at first. You ski much more down the fall line. Keep the speed under control though, their can be plenty of junk under the snow that you do not see. Start conservatively, work up as your confidence gets better and you get more comfortable.
It's good that you ski the mountain, as opposed to the park all day. This will help you adapt. Have fun, skiing steep lines in deep snow is the greatest thing in skiing.