Most all county fairgrounds in In. are run by associations that lease their property from the county or own it outright. Some are quasi goverment
groups that recieve county funds.
I think most could be considered as private property.
email them. Contact on homepage:
LaPorte County Fair July 19th - 25th 2009
Or call the fair and ask them if they have any restrictions on what in general you cannot bring onto the fairgrounds. I did not see anything on their homepage about it. Many times signs are posted at entrances.