There is a book that covers the basic same principles of Hug-A-Tree. Hug-A-Tree stresses more that a Tree is a living thing and It will keep you company. The book gives easy things to remember for younger children and cool science type experiments to help them remember principles. My kids used to ask for this book at reading time.

Lost in the Woods
by Colleen Politano

Book Description
After a personal tragedy, the author, a kindergarten teacher, decided she should do something to help her students and students everywhere to be prepared when lost. Beginning with a story to capture the children's attention, Lost in the Woods acts as a model of what a well-informed, resourceful child should do when faced with a frightening situation. The book offers several activities illustrating the safety protocols outlined in the story allowing the child to personally assess the procedures' value. The third section contains information designed to assist parents and teachers in preparing children in the event they find themselves lost.

Here is the review posted at Amazon:
As a veteren member of a Search and Rescue team, I found this book to right on target for anyone going into the woods for a picnic, a day hike or an extended outing. The basic premises of Be Prepared and Stay Put once lost will help any person young or old who is confused about where they are and how to get back. The book is designed as a teaching tool for children with "science project" ideas which help young children learn key principles about staying alive and getting found. If more people read and used the ideas in this book, Search and Rescue teams would spend more time at home and less time looking for lost people. My children love the story and don't even realize they are learning valuable life skills.