Both Morningstar and Longsword are twohanders.
All twohanders when used 1hand lose -30% to dmg and speed.
That's why I don't see the point of using 2hander from horseback.
Some twohanders can be used with a shield (like Longsword, Morningstar)
As far as I know (but I may be wrong), if you use i.e. Longsword on horseback with a shield, it loses more than 30% of dmg and speed (may be something like 45%).
But i am not sure about bolded part.