All the County radio stuff, with a couple emergency use exceptions, is digital trunk--Parks, Public Works, SO, etc. all use the same pool of frequencies with different channel identifications that the computers keep straight and tell all other radios on the same talk group what frequency to listen to (hence the transmit delay and 'beep' when it's ready for you to talk. Very complicated but when it works, a great utilization of precious frequency resources (I think they all share around forty frequencies).
As far as mounted units goes, I believe the parks still have a volunteer horse patrol; they ride around and report problems on the county radio. Not sure if it's still around as I don't go to Huddart, etc. The Woodside Mounted Patrol is a private rich boys club not affiliated with the SO- after they refused to admit women in the eighties- but they may do some volunteer SAR work. There is also an SO mounted unit--a volunteer unit of horse owning deputies and perhaps some OES-based volunteers who do 'real' stuff for the SO on occasion. I know they have regular meetings and some guys participate at functions like the North Fair Oaks Festival parade (one guy has a nineteen-hand Shire--holy crap that's a big horse!) but I don't know what else they do except SAR. I don't think you'll see the SO mounted folks in the parks.
Hope that helps.