Josh is right. Instructors run into this dilemma all the time.
--Using "left and right" is riddled with problems. Lots of people get left and right mixed up in daily life. Lots of people. "Weight the right ski to go left" is totally confusing to some folks; they can't think of both at the same time. Of course some people can keep that straight. I never use it in teaching though, because I keep having to say "the other right."
--Using "uphill and downhill" works if you are only talking about the bottom half of a turn. Most skiers can keep straight which way is downhill because it can be seen - you can point to it (although I have encountered beginner adults who have difficulty with this concept). Since many people cut off the tops of their turns, and since most people understand "uphill and downhill" so easily, those terms get a ton of use. But when you are talking about skiing with round turns that have a top that is shaped by the skier, using "uphill and downhill" becomes a problem. Here's why. The left ski is uphill at start of a right turn and the right ski is uphill at end of that same right turn. Now that's really really confusing; which foot is uphill switches at the fall line right smack in the middle of the turn.
--Using "outside and inside" works when talking about round turns that have a top half - in C-shaped turns. Describing what "outside and inside" refer to makes the most sense when someone is standing there on snow walking through a round turn. The outside foot or ski is the one that takes the outside path when you walk through the turn, or when you draw on snow the two lines your feet follow. With some practice, a skier new to these terms can tap the outside boot through a series of low-pitch turns at a slow pace, tap tap tap. Doing this pinpoints when the new turn starts. because it's when the skier switches to tapping the other boot. After doing this, that skier can tap the inside boot, then move on to tapping the inside boot through a series of linked turns. This little exercise is particularly helpful when introducing people to the role of the inside ski/foot/leg in shaping turns.