I'm a little concerned that the mods I'm running now will interfere with Dawnguard. I'm running mostly weapon/armor mods but I do run dragon related mods and TSV quest mods.

Should I remove all the mods and resave to a "clean" game?

You should be ok with the weapons and armors mods, so leave those.
The dragon related mods should be ok, but I don't know for sure.(no idea if Dawnguard edits dragons, but probably not)
But the quest mods can cause problems, so i would wait for a compatibility patch for dawnguard to be sure.

Are you talking about when the PC version releases in the future, or are you running these on your Xbox?

PC version.

I've moved this over to the mods section

Not sure about your quest mods, but I'm guessing some mods affecting dragons might need an update. Your weapon and armor mods shouldn't have any problems.

The overwhelming majority of mods compatible with 1.6 should also be with Dawnguard, I would think.

I doubt any mod that modifies lycanthropy or vampirism would be compatible