For a rule of thumb about safety and which trees to let your child climb, you can trust that most children are good at self-regulating (but you know your own child best, of course). Many families have had success with the "rule" that you can only climb trees you can get into by yourself. Once up, you'll need to come down by yourself, too, although some verbal encouragement might be needed, now and then. One of the very best phrases for helping a nervous child find their way down from a tree is, "When you get down, we'll go get ice cream."
LARGE MOTOR SKILLS
Large motor skills develop the brain and are important, even if often overlooked. Your child needs to reach, pull, lift, and move in many ways, and this has been accomplished for thousands of years before the introduction of either PE class or memberships in a gym or health club. Climbing trees is a great way to do upper body exercises without weights.
READING & WRITING
Verbal directions help children learn directionality (left & right, top & bottom), which they will need when learning to read and write. They will also learn prepositions (on the branch, beside the trunk) in a way that is much more fun than worksheets!
PLANNING & PROBLEM SOLVING
A tree will sit quietly while your child thinks about the best way to solve the problem of moving up or down the branches. Leave your child in peace and don't tell them the answers. If you do, they'll end up higher in the tree than they feel comfortable or safe. They will learn how to go higher when they are ready.
Children need chances to feel brave and powerful, but in today's sanitized world, these opportunities are few and far between. Climbing trees is one of the few chances left, so plant a fast-growing tree when your child is a baby.
Suggested books about trees