Is it just me or do some managers actually forget that people have limits? That run sounds like a disaster waiting to happen. @jones.mason's sticky note idea is way better than making people run in the rain. My old boss did something similar with a "fun" obstacle course behind the warehouse and three of us ended up with pulled muscles.
Had a boss try that once. We started a simple shout out board in the break room. Just sticky notes for small wins. People actually started looking for things to praise each other for. Went from everyone being grumpy to a bit of friendly competition to get your name on the board.