Yes, you can OC there. They can not stop you from carrying. That language is very deceptive and you may encounter a county employee that thinks that weapons are prohibited or one that will use that rule to intimidate you. Daviess County has a long history of resisting state law and the preemption of firearms regulation. The Attorney General issued an opinion on this very subject in 1996. It was a total smack down of their park rules. It AGO 96-39 and can be found at the Attorney General's website. Here is the conclusion section of that opinion.
To summarize, and to apply this analysis to the specific facts presented, it is our opinion that neither the Daviess County Fiscal Court nor its County Judge/Executive, or any other local official, can ban the possession or carrying in a public park the open or concealed carrying of firearms, except the Daviess County Fiscal Court, which if it properly passes an ordinance, may prohibit or limit the carrying of concealed firearms in park buildings or portions thereof owned, leased or controlled by it. The statutes discussed herein clearly prescribe the authority of a fiscal court in this field. Based upon this, it is our opinion that Executive Order 287-96 promulgated by Daviess County Judge/ Executive W. M. Morris, Jr., undated, was unauthorized and has no legal effect.
The Daviess Co. Fiscal Court and County Sheriff know all of this. They may not like it, but they know it. They hope that you don't know it. If you are concerned about problems, just print out that AGO and KRS 65.870 and carry them along with your gun.