The intricacies of casting spells whilst on a horse seem to have been completely bypassed as far as RM2 is concerned (and the others as far as I can see) likely because Magi would rather use a Fly spell later on than trust a creature that's likely to spook under them if things are exploding nearby.
I've checked through all the base RM2 source (Companions 1-7) and so on, but the only book that has any real mention of extra mounted combat rules is Companion III - for extra damage from a charge and the Arms Companion, which again is only for melee/missile stuff.
AL&CL has mounted combat guidelines in 5.3
"Depending upon his training and background, a mounted combatant can
use anywhere from 0% to 100% of his normal OB. This restriction is not
in effect if the horse is completely stationary."
Mounted OB = Normal OB x (Riding skill bonus + special bonuses) ÷ 100
The only modifications for spell casting on page 15-19 of Spell Law (ICE 1200) are for cover, level, casting stat, position, armour and the like - there's no mention of being mounted anywhere in the SL system that I can find, the assumption appears to be that the caster is standing still and doing their thing while the target is doing everything and anything they can to avoid it.
However there is one critical part of the rules on page 14 that is useful
Movement for all spell casters is reduced to a maximum of 10% if they
are preparing a spell, and 25% if they are actually casting it.
With this and the AL rules we can extrapolate the mounted combat rules (such as they are) for Spell Law, with very little effort - which is how I've applied them in my games of RM2. So the situations:
Casting while sitting on a standing horse
There is no penalty for doing this in AL so no penalty in spell law.
The casters isn't moving or doing anything, so all is well.
Casting while riding slowly/fast/very fast/ ...
There are two things here to worry about.
1) Casting while the horse is moving
Since the Magi only has either 10% or 25% of their movement (and therefore skill rolls) this is how much of their skill I allow for any riding checks, making casting while riding quite difficult, bare in mind that some realms (Essence) can allow the caster bonuses/penalties for using more or less hands - which will also affect their ride skill (is the caster trained to steer the horse with their knees?)
2) OB/Attack roll for any spell while riding.
Since the caster is concentrating on their spell I allow a full BAR bonus (stat+skill) for any spells (Sleep, wall of fire cast) however any directed spells like shock bolt, ice bolt are restricted by their riding skill as per AL as this is OB.
Bob the Mage is trying to ride out of town after a regrettable incident where the local tavern caught fire when he was demonstrating his firebolt skill.
As he gallops for the gate his old enemy Eric the Sorcerer steps out and starts waving his hands to cast a spell, Bob decides to show off his firebolt skill and give Eric something to distract him.
Bob is level 10 and has 10 ranks in ride (50). He has 10 stat bonus for his riding skill and an excellent saddle that gives him a further +5 bonus. Bob's riding bonus is therefore +65.
Bob is going to cast his firebolt spell in one round, so he has 25% of his ride skill as he's not doing any spell preparation (25% of 65 = +16) to make his ride check as he casts his spell.
Bob has +65 bonus in ride, so he gets 65% of his OB with his Firebolt spell to blast Eric.
If Bob had decided to cast Sleep instead then he'd still make his ride roll at 25% but he'd make a standard BAR roll to try and put Eric to sleep.
Casting while being mounted and in a melee
There's not much in Spell law for being mounted and fighting, but the horse is not going to be stationary while someone is trying to smack it or it's rider - or it won't get any DB!
Therefore I apply the same checks as if the horse was moving, but the ride check is Easy as the horse isn't going very fast.