I've used both a one- and a two-handed weapon on horseback with good results (i.e. lots of dead people). It's a bit safer I'd say with a two-hander because of the greater reach. Sword of War is an awesome weapon, both for sieges and on horse.
The trade off is that you can't swing as frequently as with for example a Long Arming Sword (that I'm currently using).
There is a one-handed weapon with a reach that almost compares with two-handers, Heavy Spiked Staff.
I never missed having a shield when I was using the Sword of War, except when faced with a firing squad in the courtyard (in sieges). But there were plenty of shields lying all around me that I could pick up if I needed it. I should mention I was wearing plate armor and had 21 strength, and some points in Ironflesh.
Edit: I forgot I had player damage reduced to 1/2 :S. I actually just realized I've never changed that since I first started playing! I changed it to normal just now. I don't know if my advice is worth that much anymore.