For packed snow and ice, probably narrower tires are probably the same, but in the deep stuff, crossing 3" tall slush piles changing lanes at 50mph, or driving in 6" of unplowed tracked up snow, I think a narrower higher profile tire works much better.
My buddy had a 1998 Echo with 185/50R15 snow tires and tried our 1992 Sentra on 155/80R13's on a cottage road with about 4" of unplowed but tracked up snow, and was astounded by how much better the Sentra was. Probably the sentra was also helped by having a bit softer roll bars and spring rates than the Echo, but they are both very light fwd mtx cars, and If we switched tire sets I don't think the sentra was going to do very well with the wider low profile tires either.
For me, dry grip isn't a concern, but I do like to have decent wet grip as well, but that's mostly compound and a narrower tire does prevent aqua planing a bit better with a tire more optimized for holding snow grip, which is some what reliant on holding snow in the tread.