Chest pockets are one of the most handy features on a snow jacket, especially if you ride with a phone. They sit high on your chest where they're easy to reach while riding the lift or standing in line, and they keep your phone warm against your body so the battery doesn't drain in cold weather. That alone makes them worth having.
They're also great for stashing a spare goggle lens, sunscreen, or trail map—things you want to grab quickly without unzipping your jacket. Most are zippered, so your stuff stays secure on bumpy runs.
The one downside: if you wear a backpack regularly, the shoulder straps can sit right over chest pockets, making them awkward to access. For backcountry riders who always have a pack on, they're less useful. But for resort days with no bag, they're a small feature that makes a big difference in convenience.