My knowledge is only off of the Carolingians/Franks but the answer is that generals generally did not lead from the front. The Franks inherited a military tradition from the Romans through texts such as Vegetius’ De Rei Militari, and by all accounts they seemed to have stuck to it in many regards.

In the Roman tradition the general was meant to not take place directly in combat, but instead to survey the battlefield, from there orders could be given to different units in order to respond to the needs of the battle. From there the units would execute their orders using horns (since a human voice would likely be drowned out by the din of combat).

So the general may not have been able to have complete control over his units, he could certainly understand what was happening in the field (ideally) and order units to respond to where they were needed. However sometimes generals did fight in combat, but this was only in particularly dire situations.

Bernard Bachrach has a pretty extensive discussion of this in Early Carolingian Warfare

Generals certainly could change plans mid-battle. Caesar's army was starting to build a camp when the Nervi charged out of the forests at the Sambre.

"Caesar had everything to do at once - hoist the flag which was the signal for running to arms, recall the men from their work on the camp, fetch back those who had gone far afield in search of material for the rampart, form the battle line, address the men, and sound the trumpet signal for going into action."

He then had to rush to his right wing where two legions had become so compacted they couldn't fight effectively and personally rally them and get them to expand their formations.

In the other direction, Demetrios led his cavalry wing in a successful charge at Ipsos in 301 BCE and routed his opponents but pursued them off the field. When he tried to return his path was blocked by elephants and he couldn't make it back to support his father Antigonos who was killed and his army routed. So leading from the front meant you couldn't control your army (just the units you were with).

But as /u/Quixxeemoto mentioned, the Roman expectations for a general was to manage the battle and his army - it was not to take part in the battle himself. For that to happen it meant things had gone seriously pear-shaped.

If you look at Napoleonic generals there are are quite a lot of differences in impact they could have during a battle. Additionally, there are many difference ranks of generals and each has a different sphere of influence. Napoleon was in command of the entire army, he would come up with the battle plans with the help and input of his marshals and senior generals. During the battle he would be mounted and had the opportunity of move about the field to get information. Generals also had aides-de-camp who were mounted officers that could carry orders and dispatches to commanders dispersed throughout the battlefield. So theoretically Napoleon could have direct control over his army. However, as seen during the Waterloo campaign, orders could be misinterpreted, lost, or contradicted resulting in entire corps not participating in battles.

Below the army's commander were the Marshals. They commanded corps of 30,000-60,000 men. Marshals like Ney and Murat did often lead from the front. Ney was known as the "Bravest of the Brave" and at Waterloo joined his cavalry in charging the British infantry squares. He had 4 horses shot from under him during the battle. Murat also lead some very daring cavalry charges during the French Invasion of Russia in 1812.

On the other end of the spectrum(and unfairly so) there are marshals like Grouchy. Following the Battle of Ligny, Napoleon order Grouchy's corps to pursue the retreating Prussians. His actual orders were, The Emperor has charged me to inform you that at this moment, His Majesty is going to attack the English army which has taken positions at Waterloo, in front of the forest of Soignes. Thus, His Majesty wishes that you direct your movements on Wavre so as to move closer to us, to link your operations and establish communication, pushing before you the Prussian army corps which has taken this direction and might have stopped in Wavre, where you are to arrive as soon as possible. Grouchy follows his orders to engage the Prussian's rear. However, he is also told by General Gerard the famous "march to the sound of the guns" i.e. go to Waterloo. The French were very close to breaking the Anglo-Allies and with an additional 30,000 men might have defeated them before the arrival of the Prussians.

Below the Marshals were Generals of Divisions (5,000-10,000 men) and Generals of Brigades (2,000-3,000). As you can see in Grouchy's orders, Napoleon tells him what to do but how he does it is mostly up to him. This is often the case for junior generals, they'll be ordered to hold a hill or assault a position, but they decide how to do it. Additionally, even if generals didn't lead from the front, almost anywhere on the battlefield was dangerous. At the Battle of Borodino the French had over 30 generals killed so the life of a general was a lot more dangerous than it is today.