Before the park was established it was envisaged that horse riding would be a permitted activity on the former "Woodlands" property (Lennon 1974). The 1997 Management Plan (Page 20) contains the following regarding horse riding:
Access is unrestricted on bridle paths and in the open riding area (figure 4). The open riding area will be extended in conjunction with the relocation of the back paddock fence. In other areas limited use only by permit, and only where the style of use is compatible with other management objectives.
Figure 4 in the management plan also shows the Sugar Gum Plantation as a proposed riding area.
The open riding area consisted of the central part of the former "Woodlands" property, together with part of the Melbourne Airport land to the south of Moonee Ponds Creek, which is no longer leased by Parks Victoria and therefore not available to horse riders. The extension of the riding area in conjunction with the relocation of the back paddock fence is described in former back paddock.
The only existing bridle paths shown in the management plan were at the Somerton Road entrance and along "Swain Street" to the north of the back paddock, ending at the Gellibrand Hill entrance of the back paddock. (There is a dirt track along the outside of the back paddock fence for management purposes, and in parallel with it a gravel track for management vehicles, cyclists and walkers. It is not clear to me which of these is considered the bridle path.) One new bridle path has been created since 1997 - this goes through the north end of the sugar gum plantation, crosses Providence Road, and then goes south to join the council reserve.
There is no up to date map showing bridle paths and permitted riding areas in the park.
Clearly, there was never any intention of allowing horses onto areas of native grass, with the exception of the strip of land outside the northern boundary of the back paddock, which was sacrificed. Horses have a negative impact on native grasses due to compaction or pugging of the soil (depending on moisture content), and due to weeds seeds contained in their dung.
If horses are permitted in some parts of the park but not in others, then there obviously needs to be fencing to enforce this. This was the case when the the management plan was written. Since then two new fences to limit horse access have been erected - one across the former back paddock area, and the other around the former Greenvale Sanatorium land. The former is ineffective because of a missing gate, giving horses access to native grasslands in this area. There are also areas of native grass to the south of Gellibrand Hill, which are currently accessible to horses because of the latest back paddock downsizing. Furthermore there are areas of native grass in Weeroona Cemetery Conservation Zone which is currently accessible to horses due to derelict fencing.