With all units, regardless of type, being positioned on a hill offers a morale boost. In my opinion, hills are more defensible than forts, especially if you are outgunned. The following are effects hills have on each unit type, and how you can maximize these effects.
With infantry: Generally, only two things should decide where you place your infantry on a hill:
2) skirmishers and any units with longer range belong behind line infantry. This protects them as well as gives you the ability to give double the normal firepower on an enemy while not damaging your own units.
2) if your enemy outguns you cannon-wise, give up the hill. The elevated ground will act like a massive trench wall protecting you from their cannon and even mortars, in most cases.
With cavalry: Having your cavalry positioned on a hill does two things:
1) exposes them to cannon fire, and
2) gives them increased charge bonus.
TIPS: Generally, I try to keep my cavalry off hills simply because they are directly in the way of cannon balls. Try to keep them just behind the apex of the hill, then try to time the enemy's approach with the moment you give the order to charge. This way, you remove problem (1) and retain your charge bonus.
With artillery: Always try to put your artillery at the apex of the hill, again for four reasons:
1) increased range,
2) anywhere else causes your cannons' trajectories to go all over the place (i.e., if positioned in the middle of the hill, they will be pointed down and will just hit your own men),
3) it's the highest point, so enemies tire out and slow down trying to reach you, and
4) at the apex they will likely be sheltered by your own men lower down on the hill, and because they are not in deep lines like infantry and cavalry, the entire unit can stretch out along the apex. This provides excellent shelter from cannon fire because the enemy cannons will have to literally hit them with a perfectly precise shot in order to take them out - any higher or lower and the ball sails over or smacks the dirt and stops.
TIPS: When the apex is unavailable (i.e., outside the battle-map) just make sure your cannon are as high as they can get.
Of course, there are inherent risks and problems to hillside combat. It makes perfect sense that soldiers will tire out when marching uphill; my suggestion is to fix this problem on the campaign map, when possible. By that I mean to position your armies on hill slopes visible in the campaign map. Obviously, it's not always possible, but when it is an option, it is definitely ideal. I use hills all the time in every one of my battles, as I am a defensive expert. I am hardly ever the aggressor in battles because I know that I can more than halve my losses when defending, as compared to attacking.
To be honest, I wouldn't know very well how to assault hills since I am better at defending them, but I certainly know that when defending, cannon, especially those with shrapnel, are the biggest threat If you leave the enemy cannon to keep firing will, you will lose very quickly. So my suggestion when fighting an enemy that has dug into a hill: get cannon, and lots of it.
At any rate, I hope this helps you in deciding how to conduct your elevated battles.
[This message has been edited by TKwarrior17 (edited 05-15-2010 @ 00:32 AM).]