New plaster over top of exposed horsehair plaster in Bathroom
Yep, you can plaster right onto everything. The Horsehair is in what's called the Brown Coat. The Brown Coat makes up almost all of the depth with the plaster just being the very minor finish. It's all quite moisture resistant too, like the rest below (no drywall can be trusted).

So, while the Brown coat's still moist where it meets the old plaster face, you'll need to scrape that down at the seam to leave room for the plaster. The Brown Coat stuff is cheap and leaving it low for more plaster is perfectly fine.

Though, for such a small room, I think you'd do much better by Tapconing (masonry screws) or Thin-Setting (Tiling compound) Cement-board (readily available in 1/4" thickness) to either fully bare walls or 2 Thin-setted layers of Cement-board where the wainscoting was.