As a primary supply, I've noticed that schools have wildly varying criteria for calling a 'wet play'. A few, very wisely, are loathe to keep the kids in and will only do so if there's Monsoon-style precipitation. However, far too many will announce it's wet play if there's just a bit of drizzle. I've also been in schools where the pupils haven't been allowed out because it's snowing (why???) and I've been in one place where they wouldn't let them out because it was too cold! Just to be clear, I teach in England, where it is never too cold to go outside for a while.
Going out and working off some energy at break times is good for the children and it's also good for the staff - it's very easy to tell when a class has had to stay in at break! It bloody infuriates me when I'm told a class has to stay in because there's a bit of drizzle outside.