I installed Dawnguard the other day and the newest update, and after a bit of messing around with my mods it seemed to all be working fine, but when I loaded my save game it loads fine, then it fades to black and when it reappears I'm floating in the air and can't move or do anything and I can't save.
It's really annoying because when I started a new game it all works fine, so it was only my old saves that had the glitch.

Is this a known bug with Dawnguard or is it maybe just a weird occurrence because of one of the mods I'm using?
I wasn't very far into it with my old character so it wasn't too big a deal making a new game, it's just annoying that I don't know why it happened.

I think incompatibile mods are breaking your saves. Did you check if their authors updated them after Dawnguard release?