Use sponge sandpaper and make sure to get it damp. I find this also gives a better finish, but it depends on what you use for mud.

Super duper lightweight premixed mud will create a dust storm no matter what you do.

Make sure to turn off you furnace/air exchanger while you are working so you don't plug it up with the dust. That stuff gums up air filters very badly.

Thanks for the reminder about the heat pump. Didn't think of that.

Cover your HVAC returns with light guage sheet metal and screw them down and have supplemental heat for the drywall crew. You probably should have addressed who pays/supplies for the cost of heating beforehand though. If you don't cover your returns they will get full of dust and the occasional pop can in them not to mention small pieces of drywall.
My HVAC installed covered them for me and I didn't even want the HVAC running until the drywallers were done..of course this was in July though but even in December I would have brought in supplemental heat before I ran the HVAC