I enjoyed this video clip of elephants at the Save Elephant Foundation's reserve in Chiang Mai, Thailand. They're Asian elephants, but they like rain just as much as (perhaps even more than) the African elephants I remember from my days on that continent.
Yes, baby elephants have fun in mud, just like human infants!
I note that zoos in the USA often seem to have trouble preventing their elephants from making mud-wallows in which to roll. I'm afraid it's a losing battle. If a six-ton elephant decides it wants a mud-wallow right there, it's going to have a mud-wallow there, whether its keepers like it or not!