The rocking horse first appeared in the video "The Corenthal Connection." It was found in a storage facility rented by Dr. Corenthal. In that video the boys find the horse inside the storage room, and then in the "timeslip" witnessed in that video they see the Doctor placing the horse into storage. Based on Corenthals words, and his reaction to the toy it belonged to The Mining Town Four.
Much later the horse appeared again in the background of the video "Hidden cameras and emails" where it can be seen rocking by itself in the corner. Speculation is that the horse is a haunted object.
In Dead end with a Pulse we see Jeff playing with the horse. Vince points out that he has been doing so for over an hour.