Your all-mountain skis can certainly handle a few inches of fresh snow, but once you're dealing with deep powder—think 8 inches or more—a dedicated powder ski makes a huge difference. Powder skis are wider (typically 105mm+ underfoot) and feature rocker profiles that help the ski tips plane up on top of the snow instead of diving underneath it. This "float" is what keeps you surfing through deep snow rather than fighting to stay upright.
That said, powder skis are a specialized tool. If you only see a couple storm days a season and spend most of your time on groomers or mixed conditions, a powder ski will feel sluggish and hard to control on firm snow. They're best for skiers who regularly chase fresh snow—whether that's at a stormy resort, in the backcountry, or on dedicated trips to places like Utah or Japan.
Be honest about where you actually ski most days. If deep powder is a rare treat, a versatile all-mountain ski with some tip rocker will handle light powder days just fine while still performing everywhere else.