All my children, and grand children, have climbed trees. We have one in the back garden that has been grown and pruned especially for climbing. It is also sporting a very unattractive but quite helpful scaffolding to give better hand holds for safer climbing.
Watching the girls climb still makes me nervous though - especially when they're in dresses. They regularly have slipped holds and missteps and fall out of the tree and onto the grass below. They keep getting up again though; climbing up into the branches; learning about balance and strategy and how monkey swings and all that jazz.
One game that Dylan loves is Teddy Rescue. Her teddy is wedged high up into the tree and she has to figure out how to save Teddy. She *loves* this game. Especially the bit where she drops Teddy out of the tree once he's been rescued.