Cool mule pic! I think it's really special when a horse or mule trusts you enough to let you get that close when they're laying down. They're at their most vulnerable at that moment and they're basically trusting you with their life. All the young ones that I've raised will let me get that close, but the older ones are more skeptical, unless they're sick.
Bay will stay down if I come up quietly, and Cyn will drop right in front of us to roll... The pony will stay down in her stall if we're in the barn, but not if she thinks we're gonna open her gate ;~D
Hoagie's funny in that he's stubborn and persistant about getting to lay down. Bob often goes on club rides and overnight type rides where there's a lot of social time before going home, and Hoagie always lays down, even with the commotion of a lot of trailers and other horses around.
When Bob went away on a trip recently, his farm sitter called and said Hoagie wouldn't get up. Bob said, well, call the vet out if you're worried, but I bet he's fine, he just doesn't like being told what to do, he gets up when he wants to! It's just such an odd behavior, and worrisome to most horse people to have an animal that doesn't want to get up when you approach.
He was fine...