The one place I was not really lost, but felt like I was rambling a bit without getting anywhere was Powder Mountain, UT. As you may know that place really sprawls!
Normally, and my son can attest to this, when I'm visiting big, new ski areas I am constantly looking at trail maps on the lift, on the slopes, and in the lodge. Since I like to write trip reports about our visits I pretty much want to know the name of every trail I ski. This seems to reinforce my memory and prevents ever feeling lost at a ski area. I can recall almost every run taken during a given ski day, at least for a few days until I can jot down some notes.
Having said that, I can frequently get separated from friends/family when I am skiing because I'll make unexpected stops for photos, to yak with strangers, or because I'm just slow. I don't generally carry a cell phone. This can present some problems at a big ski area. Not cool to get separated in a large glade like Casablanca at Saddleback, then have other members of the party waiting for the straggler at bottom of hill to make sure they aren't hurt. Also this winter, at Steamboat I got separated from my son when we took different turns at a fork in a trail. After a couple of hours of separation I finally caught up with him because we both had planned to join a Billy Kidd clinic at a certain time and place and that's where we reconnected.
The remarks in this thread from Europeans are interesting to me. I made a ski trip Austria in 2003 and wrote a story about it. We visited five different, large ski areas and had given them a heads-up that we were coming. Each ski area provided a guide. I thought it was simply a nice gesture, but now I suspect it was to make sure I didn't get lost.
Funny thing, if I am led around a ski area by a friendly local or guide I don't remember nearly as many details, but probably have a better, more carefree time just enjoying the experience.