Lay a tarp or large rag on the floor below the hole in the horsehair wall to protect the floor from abrasive plaster pieces and dust.
Remove loose pieces of plaster from the edge of the hole by hand.
Rub a plaster rasp over the edges of the hole to smooth the jagged lines around the entire perimeter of the hole.
Sand the area of the wall extending 3 to 4 inches from the hole with 60-grit sandpaper.
Vacuum the dust off the lath and edges of the hole with a shop vacuum.
Cut diamond-shaped metal lath to the size of the hole if the hole is more than 4 inches wide. Tack the metal lath to existing wood lath with galvanized nails every 2 to 3 inches around the perimeter and in the field of the hole. If the hole is smaller than 4 inches wide, peel a self-adhesive fiberglass mesh patch off the protective backing and affix it to the wall over the hole.
Mix plaster with water according to the manufacturer's directions in a bucket.
Brush an epoxy-based plaster-bonding agent over the metal lath or fiberglass mesh.
Scoop up plaster on a margin trowel. Apply a 1/8-inch thin coat over the metal lath or fiberglass patch. If you are applying plaster over a fiberglass patch, extend the plaster past the hole, completely covering the patch. Let the plaster set up, but not dry. Plaster is set when it feels hard and does not give to the touch.
Spread a second 1/8-inch layer of plaster over the hole with the margin trowel and let it set up. Continue to add wet plaster to set plaster in 1/8-inch layers until the plaster sits slightly higher than the existing horsehair plaster wall. If you are applying plaster over a fiberglass patch, apply a second 1/8-inch layer of plaster over the patch, extending and feathering the plaster 1 inch past the patch. Let the plaster dry for 24 hours.
Sand the patch to make it even with the existing wall with 100-grit sandpaper.