The most important points to remember about what to wear are:
Gaiters are required. Worn properly, with a cinch at the top and secured at the bottom, they keep snow from entering the top of your boots. This is both a safety factor and a comfort factor. Why safety? Because snow entering your boots melt and cause your foot to then lose heat. In cold conditions, this can become a risk. Gaiters do not need to be expensive or made of Gore-tex.
Layers and breathability. Backcountry skiing can generate surprising amounts of body heat and it won't be long before you'll want to be wearing very few thin layers. A thin breathable shell on the outside is advisable.