Full-length base layer bottoms that extend to your ankle are the most common choice for skiing and snowboarding, and for good reason—they give you maximum warmth and complete leg coverage under your ski pants. They're ideal for cold days when you want every inch insulated.
The main thing to watch out for is bunching at the ankle inside your ski boots. Extra fabric wadded up in there can create pressure points and even restrict circulation, which makes for cold, uncomfortable feet. Look for full-length bottoms with stirrups that loop under your foot to keep the fabric pulled down and smooth, or make sure the hem fits close to your ankle.
If you have custom-fitted boots or are prone to boot discomfort, you might prefer 3/4 length bottoms instead. But for most skiers, a well-fitted full-length base layer with stirrups works great and keeps you warm from waist to ankle.