A ski gaiter, a ski mask, or a ski neckwarmer is very important. With your neck and face protected from the cold air and the harsh wind, you'll feel a lot warmer.
Obviously, ski gloves or mittens are necessary. Think twice before you purchase a random pair of inexpensive gloves - cold hands can really ruin a ski day, and investing in a pair of warm, durable ski gloves that truly keep your hands warm is definitely worth it.
Ski goggles enhance your vision on the slopes and are a barrier against the cold and wind, too. On warmer days, sport sunglasses may be an option, too. Make sure ski goggles are part of your skiing wardrobe.
While cross country skiers may opt for a hat, a ski helmet is necessary for downhill skiers. With today's modern, attractive helmets, there is no excuse for not wearing a helmet. You can still have fun with a helmet, too - coordinate to it your outfit (ski helmets today aren't just black or silver, but they come in a multitude of colors) or cover it with stickers from your favorite ski resorts. It shouldn't even be a question - why risk a head injury? A ski helmet is necessary for safe skiing.
Your average athletic cotton socks aren't optimal for skiing. Cotton absorbs sweat and makes you cold. Wearing one pair of socks designed for skiing is best. Knee-high, technical ski socks wick away moisture but provide insulation, as well.