There are a number of techniques with various weapons that are meant to be done with two hands, though by and large one hand is typically on the reins, with the left hand letting go occassinally. The majority of these techniques, though, are meant to grasp the weapon like a spear, even a sword (i.e. half-sword techniques). Note, though, that the Paulus Kal manuscript illustrates mounted combatants with longswords with long, two handed grips, though clearly they are being used one handed.

http://mdz10.bib-bvb.de/~db/bsb00001840/image...l?seite=30

The third guard of mounted combat (rossfechten) from the anonymous author of the von Danzig treatise is described with two hands:

"Position yourself for it thus: grasp your lance in the middle with both hands and hold it across before you on the saddlebow so that the point remains on your left side, and ride to him in this manner."

And the fifth guard for the sword:

"When you sit upon the horse, then hold your sword with your right hand at the grip and with the left hand gripping the middle of the blade and hold it across before you on your saddle."

Note that you can still hold the reins if necessary in this guard, though the reins will likely be dropped as soon as fighting commences.

And the author also makes this comment:

"...from all three guards youu should come with the left hand to help on the lance if you want more strength." (that is, you should let go of the reins to put both hands on the weapon)

This last part is technically for the lance, though the same could easily be applied to the sword, since it is all within the same art.

Gavin Kisebach wrote:

The illustration of halfswording seems to support the notion of using the horse's inertia in a linear attack, and the notion that heavy armor would be a highly advisable component of this weapon system.

Actually, a number of the mounted combat techniques are meant to be done while the horses are not moving or moving slowly, just as a number are intended to be used as the horses are racing to each other. (and Mair's treatise has a number of things that spring straight from earlier treatises as well, in many cases re-illustrating sections of earlier treatises that are "reborn" in his contemporary style). Here's an example from Sigmund Ringeck of a rather slick technique that won't work if you are charging in full throttle:

"Note, when you come with your left side to his rigth, if he has his sword drawn and moves forth to strike grab his right arm behind the elbow with your left hand. And push him upward while raising your left foot up under his right beneath the stirrup leather, so that he falls. Or, when you have grabbed with your left hand behind his right elbow, hold the arm fast; and grab the pommel of his sword with your right and and so take his sword..."

Regarding armour: Yes, it probably was advisable to wear heavy armour in this style, but the 1467 edition of Talhoffer shows the mounted combatants with no armour at all. So armour wasn't necessarily a given.