The machines look like they are coin operated but they don't need money to work. Just push the coin lever in and go.
There's a laundry room near each of the four pools. Access to Congress Park and Grandstand is probably the closest. They border the pool and have windows facing out at the pool so you don't need to be in there the whole time. We usually just take our laundry with us and run loads while enjoying the pool for a few hours.
The main pool (High Rock Springs) has a laundry room a little further away, down the outside corridor beside Community Hall. It's bigger but may give you a queasy feeling of not being able to easily watch your stuff. You can not see the room or its entrance while in the pool area. Nonetheless we've washed closed at both CP and HRS pool areas and not had any issues. In fact, I came home with an extra Disney sock last trip. Musta gotten stuck in the dryer.
All the laundry rooms have TVs as well to keep you occupied, and tables for folding and chairs. They're air conditioned as well. Laundry supplies are available in vending machines. $1-$2 each? We bring our own.