The horse on bow rockers that we know and love today was a product of eighteenth century England and were popular with the wealthy with it being said they were used to help develop children's' balance for the riding of real horses.
Horses in this period were carved, roughly rasped and then covered with gesso which was also known as whitening and looks like plaster. This was far easier to rub down than the wood itself and gave a very smooth finish on which to paint. Was a very time-consuming process communications the gesso was applied hot, in multiple coats, with sanding in-between and each coat could take up to ten hours to dry.
A delightfully untouched example that would grace any space.