Quote Originally Posted by BigTex
A claymore is a 1hd scottish cavalry sword. What your refering to is a cleavemore (sp). But almost any 2hd combat technique involves balance and two feet on the ground to build and maintain momentum and parry.
What !?
Even a basic google search for "claymore sword" will return thousands of results which define claymore as "two handed sword used by highlanders", with pictures and everything. Google "cleavemore" returns exactly 3 results, one of which is at the .org ... The term "claymore" refers also to a type of scottish one-handed sword, but that usage is far less common and it's a weapon that only came into use around 1700-1800, not our period of interest.

As to the original topic, the only sane way I can imagine using a large 2h sword would be to swing downward with one hand, along the side of the horse - imagine a polo player with a mallet hitting infantrymen en-passant. Trying to use it with both hands would result, as other have pointed already, in either the horse losing important parts of his anatomy, or the rider falling off if he leans too far on one side to avoid hurting his mount.