Does anyone know if you can still dual-wield?
Good question. Anybody??? I would venture to say no
If you have two 1h weapons equipped you still only swing with one arm.
Left clicking makes you lean off the horse and swing to the right of it. Right clicking makes you swing off the horse, leaning the other way but still using your primary weapon. They're reversed like when normal dual weilding which is still a bit odd for me.

The video made me laugh, because thats about the only time you would have mounted combat... Is when you attack guards..... 80% of the time your wandering around there is nothing.......
You could fight animals in the wilderness, I chased down a couple of Elk. It made killing them 100x easier.
Also I'm only fighting guards because I needed to buy a horse and Whiterun is the most convenient place I know.