Some small airports don't have fences at all. It doesn't mean it's OK or even safe to wander around the ramp with kids.

We parked our Phenom 300 at Marfa, TX back around 2016 and there was no fence at all. Anyone could have pulled off the road and walked right up to the jet. I was surprised the company let us RON there.

Check the FAA’s 5010 Airport Master Record. It will confirm the airport’s status, such a privately owned; etc.

The other thing to consider is who owns the ramp. I instructed at a public airport, but our flight school leased an area of the ramp and hangars.