There is a multitude of great kids’ ski jackets on the market these days. Your youngster should definitely be the one to pick the style — they’re the ones that’ll have to feel comfortable and “cool” wearing it — but you should make sure that the jacket fulfills the basic quality requirements. Jackets should always be at least water-repellant, or better yet, water-resistant, and even better waterproof.
The best combination is waterproof and breathable. You may find some very cheap jackets that are labeled "waterproof" but there may be little to no breathability. What will happen is that the fabric may keep the water out, but it will also keep the sweat in. That moisture, especially on a jacket with cheap insulation, will soon feel uncomfortable and your child will likely become chilled.
“Waterproof” means that water droplets are prevented from entering the fabric, whereas “breathable” means that water vapor will be able to move back out through the fabric. There are actually US standards for what can be determined as waterproof or breathable. Breathability is measured in grams (grams of water vapor per square meter of fabric per 24 hour period) and waterproofness is measured in millimeters (amount of water, in mm, that can be suspended above the fabric before water seeps through). Without getting too technical here, the rule for both is the higher the numbers the better.
Water-resistant and water-repellent fabrics generally breathe better than the full-on waterproof versions. However, some of the water-resistant jackets listed here will do a great job keeping the moisture out, while some of the waterproof jackets offer exceptionally high breathability. If your kid only does a two-hour ski lesson once a week, a water-resistant jacket will do the job, even in heavy snow or rain (but who wants to ski in the rain anyways…)
Zippers can be the weak spots on any jacket and therefore the best jackets offer fully sealed seams. However, zippers can also make a big difference in how breathable the jacket will be as they can be opened to let more fresh air inside. Also, make sure the jacket has good cuffs at wrists and waistline because they will seal the jacket and prevent cold air and snow from coming in.
Hoods are great and ideally you should be able to roll them up or just have the ability to take them off when they’re not needed. Hoods that can’t be detached or stuffed inside the collar can become filled with snow or rain.
Last but not least, fit is very important. Your child should be able to move freely when wearing the jacket and not be restricted. Don’t buy the jackets too baggy though, because they’ll get in the way of good form.