Short answer is no. The park doesn't generally have a duty to protect you from anything, short of dangers it creates, or hazards it conceals. As others have mentioned, the government doesn't even have an absolute duty to provide police protection. If you read some of the cases, this is more a practical matter, in that it would be impossible to prevent 100% of the crimes committed.

The distinction is that you are there voluntarily. If you feel a firearm is the only way you would feel safe, and firearms are prohibited, don't go to the park. It's much different in cases where the government compels people to be somewhere (schools, prisons etc.)