Do I remove cornice when I'm getting rid of horse hair plasterboard walls?
Normally I would remove the cornice and replace it once the drywall is finished and painted - because that is usually the easiest, if you are okay with installing new crown molding.

If that's something you aren't interested in doing (perhaps it's a molding you can't copy and don't want to get rid of), then you can finish your job without removing it. First, remove the plaster down to the studs, from the floor to about an inch below the cornice. Then nail strips on each stud to shim the surface of the drywall out to the surface of the old plasterboard which is still visible under the cornice. Plaster is generally about 7/8", and if you're using 1/2" drywall, that would be a 3/8" shim the length of the stud. (You should measure the plaster thickness in several places to be sure of this thickness, though.) Rip 2x4s into a lot of 3/8" x 1-1/2" strips and cut to the length of the studs. 4 penny nails are sufficient for tacking these shims onto the studs.

Then, hang the drywall as normal. Use 1-5/8" screws so that you grab the studs behind the shim strips. When taping, run tape right up against the cornice all around the room. Then finish as you would finish any butt joint, feathering down twelve inches or so.

Once sanded and painted, no one will ever know that there is plaster behind the cornice.