Trails
There are some trails but not very many. All together I am thinking less than 1 mile. But each trail either leads to a cute picnic area or to a field that looks fun for playing ball, etc. My 18 month old son walked most of the trails with me and only got tired near the very end.
Playground
None
Other
Tons of people had their dogs out playing in those fields - some even off leash. The real gem of this place are the gardens. While we were there in January, there was not much to see, but I cannot wait to go back in Spring and Summer - you can tell they are really magnificent. The Master Gardeners of Cobb County take care of those. Take a picnic when you go. Also, you can see some old stables, a bee keeping area, and the old farmhouse which is the home of the caretaker now. This place is small, but we ended up spending an hour there on a blustery day because there was so much to see. It is in such a remote area that there are hardly any people there also, which is nice.
Pictures
The website has much better pictures, but I wanted to show the stables, some of the garden beds, and the way the trails are made. We used a regular stroller (not the running stroller) and it was fine to navigate.