Mounted combat and two-handed weapons

[phiwum]

A horseman can carry and use any weapon for which he
has the ST, including missile weapons, thrown weapons, and
polearms. A horseman may “jab” with a pole weapon, just as
though he were on foot. A horseman charging does 1 die extra
damage if he hits with a pole weapon, and takes 1 die extra
damage if a pole weapon hits him.

Really?

I guess I know that one can fire a bow from a horse, but I'm having trouble picturing a rider using a two-handed melee weapon (halberd, two handed sword, etc.) from a horse. In fact, using a bow without the horse running straight at the end of its movement or slowly is a little hard for me to imagine.

Now, I have little imagination, so someone knowledgeable can tell me whether this sounds right.

Thanks.