What about an army-based officer (aka general) system instead of a squad-based one? In order to put together an army above a certain, small size, you need to recruit or appoint a general to lead it. Scouting and raiding parties, and patrols, for example could be small enough so that you don't need to worry about it. But anything that could actually be called an army would require an appointed general or leader, really whatever you want to call it.
There could be several ways to appoint a general, too, and the different ways could have pros and cons.
1) You could elevate one unit of the army to be the general (he wouldn't appear as a separate unit, it should be abstracted above that).
Pros: units of the same type get an extra bonus
Cons: different types of units get a smaller bonus
2) You could send some abstract military administrator or whatever to be the general (likewise, wouldn't appear as a separate unit).
No real pros and cons, everybody is treated equally in terms of bonuses and the like
3) You could appoint a hero. This time, he would appear as a separate unit.
Pros: would depend largely on the hero but should usually be a better general than the other two options
Cons: can actually die in combat, plus other possible hero-dependent cons.
In all three cases the generals would improve with combat experience. I'm not sure if I like this idea or not, but I thought I'd throw it out there for others to kick it around.
How can you be ambivalent of such an awesome idea? I mean, come on, your idea is made of win.
Back to topic: my opinions are as follows.
1) Squads come hand-in-hand with a squad leader and a flag carrier. This is purely cosmetic. Except for the flag carrier, which should help a lot when trying to find a specific squad.
2) The squad level up and get both a standard increase to attack/def/hp and a specific bonus chosen by the player. Available bonuses are determined by the player's technological and/or magical level and by the type of the unit (cavalry/infantry/ranged/caster etc.).
3) Non-fantastic units can be both re-equipped and re-trained. Re-equipping a unit is just changing their bronze swords to iron swords. The cost is just the new equipment that needs to be made (the old equipment get stored). Re-training should work exactly like pigeonpigeon described it.
4) Equipping squads with magical items should be a given. It's just expansive.
5) When a certain squad get rediclusely experianced (you know what I mean), it becomes an 'elite squad'. This is NOT a cosmetic change. Elite squads are halfway between heroes and standard units. They get a totaly different selection of bonuses, a name (The Gleaming Pikes or The Thunderhoof Squad) and most importantly, can be given 'special missions'. The special missions available depands on the unit's type and on the elite bonuses it recieved.
6) Special missions: actions that can be executed through the overland screen. It's like sending an elite squad on a special ops. mission. The squad must have the needed bonuses to execute the missions. Some missions may also fail.
Example #1) infiltrate an enemy city (during siege). When the battle starts, you will have the elite squad inside the enemy city. Requires: [Inflitrate], can only be executed by infantry.
Example #2) bodyguards, assigned to a specific overland character (heroes mostly). When the character is drawn to a fight, he will have the elite squad surrounding him and they will act as a single unit. Requires: N/A.
Example #3) Capture an overland character (big monster/hero/diplomat etc.). You can't expect a regular unit to capture a hero alive, but it is possible for an elite unit. Requires: [Capture], cavalry or infantry only.
I hope you understand what I mean with the idea of elite squads. Opinions?
P.S.: Maybe all caster units should be considered as elite squads?