OK...there are a few misconceptions here. First, Lances, spears & bows being "2-handed weapons" have nothing to do with the question as I understand it. While all 3 are in fact "2-handed weapons" all are used mounted but not in the same way a 2-handed sword or battle ax would be.
Let’s keep in mind that the use of the lance as commonly portrayed was only made possible by the advent of stirrups. Prior to this, mounted warriors would use relatively light spears held in an overhand grip for thrusting downward with.
Bows are used mounted...but only specific types of bows, mostly shorter in length (It would be fairly difficult to use an English long-bow or typical pyramid bow from horseback. Yes, I am aware that the Japanese Kyūdō can be used mounted and it is a relatively long bow, but you should also note that the bottom limb is shorter then the top limb, which facilitates its use while mounted.
Finally, there are no historical records of 2-handed weapons being used while mounted on anything near regularity. Keep in mind that most 2-handed weapons were developed and used in specific circumstances, none of which were mounted. Simple body mechanics and physics would prevent these weapons from being used without some pretty hefty penalties (that is why such weapons were not used this way in the real world). That being said, yes, allow them to attempt it and apply very hefty penalties (a ride check would NOT in any way negate these penalties because it is not an issue of riding).
As far as the argument that the rules do not prevent their use...well, there will always be meat-grinding ROLL players who will try to gain every possible advantage that the rules do not prevent ("wow...think of the damage bonus for a mounted charge with a 2-handed weapon" they think gleefully), however, it is up to the GM to make sure that the game world reflects the realistic parameters dictated by the laws of physics and physical probability.
Just saying