When you're earning your turns, every ounce counts. An AT ski is significantly lighter than a powder or big-mountain freeride ski, so it won't hold you back on the ascent. The downside of the light weight is that you might get tossed around a little more by variable conditions, so again: find the balance that works best for you.
As with alpine skis, you'll find a lot of variation in width. Narrower skis will be faster on the ascent but may sink into deep snow, while fat skis with 105mm+ waists will be slower going up but float more easily in powder. Again, it's all about a balance of uphill speed and downhill performance.
You can for the most part expect a blend of camber underfoot and either tip-and-tail rocker or early rise in an AT ski. This adds a touch of surfy maneuverability for deep snow and tight terrain, without sacrificing the edge hold you'll need if you encounter hardpack. But you can also find full-rocker and traditional camber models.