Well, first you have to remember that only licensed vehicles, insured, and inspected are allowed in Freeman Park. Aside from that, there are very limited places to park at all, much less a trailer overnight in close proximity to the entrance to the park.
There are shopping centers, etc. nearby that may cater to the RV crowd, and which might allow such, but you'd have to inquire on your own.
This has been a limiting factor for some of the CNC folks over the years, but we've come to see this as a day or two on the beach to relax and enjoy activities other than trail riding.
Hope to see you on the sand!