Upvote:2
Square formation operates in an open space, where one has more efficient means of targeting it - e.g., the artillery shells, which can be fired from a greater distance and carry a more significant explosive charge than hand grenades.
Hand grenades are more suitable in close quarters - against trenches or buildings, where artillery either cannot be used or inefficient due absence of direct sight.
Upvote:8
Grenades were notoriously unreliable and short range. A modern hand grenade can be thrown between 20-40 meters. A soldier is required to throw it +30 meters. Grenades in the 1800s were heavier, thus the throwing range was shorter. It wouldn't fragment as well as a modern grenade.
That means that a soldier had to get very close to throw his grenade. So close that he was likely to be shot (or bayoneted) by his enemies.
Grenadiers were elite soldiers, because of the danger of their work. Doing that on an square would not be dangerous but suicidal.
The question also asks about horse grenadiers throwing grenades from horseback. I'm not aware that ever happened. Units got promoted/demoted to a certain status or where assigned a different title. For example, lancer units were more expensive than hussar units. After the Napoleonic wars many lancer units were renamed in hussars to save money. They of course lost the lance, but apart from the lance they were doing the same work.
The idea that a grenadier rides in on horseback, lights his fuse, tosses the grenade and hopefully escapes alive is more a gaming feature than something that happened in real life. I have never heard of it.
Given the fact that grenadiers à cheval were big men on big horses looks more like a heavy dragoon unit got promoted in title and or status. The tasks for grenadiers à cheval and cuirassiers were identical (shock cavalry), the difference being cuirassiers wore a cuirass and grenadiers à cheval did not.