A little background information to help put these comments in perspective:
Horse speeds; Walk (3-4mph), Trot (8-10mph), Canter (10-17mph), Gallop(~30mph, modern horses have been clocked at up to 50mph for quarter mile). I appreciate that for horses of the ancient era, carrying a rider the speeds may be reduced.
Human speeds; Fastest ever sprint (anaerobic) (26.7mph), Sustained run (15mph - equates to 4 minute mile); Again, for ancient era carrying light weapons and the speeds may be reduced.
So, broadly speaking, a horse is twice as fast as a man and probably could sustain the speed for longer too.
In the notes below I'll use the following notation;
LC : Light Cavalry (LH and Camelry) - 4 MPs (I'm writing this from memory at work, so forgive me if Camelry is 3MPs - just include them with the HC)
MC : Medium Cavalry (Protected and Armoured Horse) - 4 MPs
HC : Heavy Cavalry (Cataphracts and Elephants) - 3MPs
The basic problems
Cavalry attacking Skirmishers (LF)
It seems totally unrealistic for cavalry not to be able to catch and engage LF. However, I do appreciate that LF has a role to play, so it shouldn't be so simple that if it is in range it is attackable because the LF would see the cavalry coming and would run away with a head start. So my proposal is as follows:
Basic Rule 1
If the LF are 2 hexes away they would be caught if they tried to run (probably by the 4th hex given horses are twice as fast), so rather than be caught running away with back to the enemy, they stand and fight.
If the LF are 4 hexes away they would not be caught, so they evade. the cavalry finishes the move on the hex that was occupied by the LF.
Optional Rule 1
If the LF are 3 hexes away they probably wouldn't be caught, so they evade. Optional Rule 1.1 The cavalry finish their move on the hex vacated by the LF. Optional Rule 1.2 The cavalry finish their move one hex further in the line pursuing the LF.
Optional Rule 2
If the LF are 3 hexes away they probably wouldn't be caught if they are efficient. A test is made which is biased in favour of quality and / or training, to determine whether they evade or fight. This represents the speed of spotting the danger, relating it to the officer, a decision being made and the troops reacting to commands. Highly efficient drilled troops would do all this much quicker than poor undrilled troops. If the test is passed the LF evade. If failed, they stand and fight. Optional Rule 1.1 and 1.2 could apply to the evade here too.
If it was desirable to try to be more selective then we could have different variations for LC , MC and HC to reflect the different speeds. So, for example, HC never catch 3 hexes and use optional rule 2 for 2 hexes (or maybe never catch at all) and LC always catch 2 and 3 hexes and use optional rule 2 for 4 hexes.
By use of optional rule 1.1 then it would still give LF a good role to play in slowing the advance of cavalry by limiting their rate of advance.
By implementing this rule a further rule would probably be required for the movement of LF. This new rule would be a test to see if LF follow orders when moving within melee range in front of cavalry. The factors that would affect this test are commander presence, LF quality and training, e.g. drilled superior troops are more likely to follow orders than undrilled poor troops. If they fail the test the troops go into anarchy status and do not move.
Cavalry bypassing Skirmishers (LF)
Again it seems unrealistic to me that skirmishers can stop or slow cavalry, particularly the MC, without engaging them. A line of cavalry is charging and you either stand and fight (ouch

Basic Rule 2
If only LF are 2 hexes away and blocking the path of the cavalry (LC or MC only) then cavalry can move to all hexes behind the LF that they would normally reach (this is selected as a normal move display by clicking on the target hex). However, a test would be required to do so.
1st Test: To see if the cavalry follow orders to charge through the line. The factors that would affect this test are commander presence, troop type, quality and training. It seems reasonable to me that more armour, better quality and drilled are more likely to follow orders to charge through the line. For example, I can't see Alexander's companions refusing to charge through a line of slingers. If this test is failed the cavalry go into anarchy and refuse to move.
2nd Test: To determine whether the LF yield the ground and allow the charge to pass through. The factors that would affect this test are commander presence, LF quality and training and the troop type and quality of the cavalry. Better and more disciplined LF may resist harder. Better cavalry would be resisted less.
If the LF pass the test they stand and fight and normal melee rules are followed. If the LF fail the test there are 2 options, which could be determined by a percentage roll, or one options could be chosen to apply in all situations.
Optional Rule 3
The LF evade following normal evade rules. The cavalry move to their destination hex.
Optional Rule 4
The LF stand their ground and the cavalry move through to their destination hex. This could mean that the LF are now cut off from their force, and this could be a pro or a con to either side. Passing through the enemy is unlikely to occur without some cost to both sides. Since the purpose of the cavalry charge is to break through, not engage, then the damage to the LF should be reduced. Similarly, since the LF are not actively opposing the charge, i.e. they are not holding their ground, then they would not inflict full damage to the cavalry. In this situation I'd suggest that a fraction of normal damage be inflicted to both sides, e.g. 1/3 of normal melee damage. The best fraction could be determined by discussion and/or play-testing.
Personally, I prefer optional rule 4 because it seems more realistic and allows the defender to inflict some damage on the cavalry while yielding the ground without troops being engaged in a death-fight.
Another discussion point may be whether it should be possible for cavalry to pass through LF to engage troops behind them. My views on this are;
If LF have troops to their immediate rear then normal LF evade rules would apply and the cavalry attacks the unit to the rear. This is the current situation.
If LF have LF 2 hexes behind them then pass through (or is penetration a better word?) is allowed. The 2nd LF would evade (see basic rule 1) and the cavalry would finish on the desired destination hex.
If LF have non-LF 2 hexes behind them then pass through is allowed. The cavalry engages the non-LF in melee and the LF, which are now behind the cavalry, are considered engaged in melee on the following turn (consider it like a unit chasing a routed unit ending its turn next to LF - if attacked the same turn it evades, if not, it must engage the following turn).
I think this improves the situation for cavalry and yet still allows LF skirmishers to be effective, although in a different way. LF can still be used to slow advance, but with the cost of either taking damage (and giving it in return) or being engaged in melee by the cavalry. If optional rule 1 and 1.1 were used then it would slow cavalry advance and ensure that LF could never be forced into melee (except after an evade, as current rules) unless the commander choses to place them in a position where it may occur (i.e. 2 hexes in front of light or medium cavalry).
All thoughts welcome
