As was covered, "helmet toppers" for the medieval period were heraldic in nature. Mostly used in tournaments, they probably saw some use on the battlefield, but I'd wager not a whole lot - it's excess weight and target with little practical purpose. The more wealthy may have worn it for show and authority, but the common soldier probably did not.
Romans, I don't really know much about. Taking a complete guess, would they have a "team color" where the soldiers of the same army all have blue, or red, or something? Again, completely guessing.
I doubt the vikings had horns. Their armor wasn't very advanced, and attaching horns that don't serve any purpose other than confusion/intimidation seems like something they wouldn't care for at a practical level. As with crests, it's an extra "target" of sorts, and probably more liability than usefulness.