Yes. In fact it can still cause more damage that it would do from foot.
On foot, with a two handed axe I usually see perhaps 40 - 50 damage, with an average speed bonus of 3 - 5% (standing still). Generally, it requires two hits to kill a low armoured enemy.
The same character on a moving horse averages 60 damage, usually with around 70% or higher speed bonus. Highest I've seen was 80 or so damage. Generally, its a one hit kill on the same kinds of enemy.
The weapon is slower when swung from on the horse, but I think the extra damage makes up for it. Of course, the fact that your more likely to strike the opponent's head from horseback probably helps. I'd say the only real disadvantage is the speed drop, but if you can tolerate this the damage gain more than makes up for it.