http://www.roadsideamerica.com/tips/getAttraction.php?tip_AttractionNo==932 quotes the following:
"The story behind the tree goes as such: A young couple camped there on their wedding night and got into a tiff. The woman said she was gonna walk away and the man said, "If you do, you'll have to walk barefoot," and threw her shoes in the tree. Then, the man got in the car and drove to Middle Gate to have a drink at the bar. The bartender talked him into going back to his wife, which he did. A year later, they brought their first child's shoes to the tree and tossed them into the branches. Since then, people have been adding and removing shoes from the tree so that when you drive over a hill on that ver desolate road, all that you can see is this cottonwood tree with shoes hanging from every branch."