Insulated gloves or mittens help your kid stay comfortable so they can stay outside longer. Because of their design, mittens for snow play often feature more insulation than gloves so they're warmer, but at the expense of dexterity. Synthetic insulation is usually used because it performs better in wet weather.
For skiing, snowboarding, or long sledding sessions, look for a glove or mitten with either a waterproofing insert (Gore-Tex, Outdry, etc.) or at a minimum, a waterproof coating on the fabric. The longer they will be out in the snow, the more advanced the technology should be. Fleece or knit gloves and mittens should be reserved for cold, dry days.
Since dexterity is often not an issue with this age group, mittens are a good choice, and they're easier for adults to put on little hands. Wrist straps or cinches can help keep them on their hands or even attached to their jacket. Many toddler gloves use an extra long gauntlet for coverage and full-length zipper for easy on and easy off.