Because of changing weather conditions, and depending upon your level of activity, layering clothes is recommended. Be aware that MORE is not necessarily better, and in many cases wearing too much clothing can be physically limiting. Follow these guidelines:
Start with a comfortable, breatheable base layer like thermal underwear, merino wool, etc.
Wear only one thin pair of socks (merino wool is optimal since it wicks moisture away from your feet and is very warm). This is important! Wearing thick, bulky socks or multiple pairs of socks restricts circulation, creates pressure points and does not allow your feet to breathe.
If it is especially cold, you can add a sweater or fleece over your base layer. Wear something that is easy to shed if the sun comes out and warms things up.
Waterproof outerwear (pants & jackets), especially for beginners who tend to fall a lot. Jeans and sweatpants get wet quickly in snow and will ice up. Skiing or snowboarding is a lot more fun when you are warm and dry!
Waterproof gloves or mittens will keep your fingers toasty warm. Knit gloves will get wet after falling only a couple of times, not so fun. Be sure your children have waterproof gloves/mittens as well.
Goggles or UV protective sunglasses/eyewear. Snow is a natural reflector of sunlight. Without UV protection your eyes (cornea) can get a "sunburn" which feels scratchy and uncomfortable. Like skin, repeated cornea burns can cause long term damage. So take care of your eyes - wear sunglasses!
Don't forget a warm beanie, hat or helmet to keep your head warm! There's a lot to be said about having a warm head when it's snowing outside, so be prepared and bring your helmet, hat or beanie!