Some of the rides don't allow you to carry anything on but provide nearby lockers to store them in. Please follow the advice of putting your bag in a waterproof bag on the water rides.
I was caught in a heavy downpour in this country and it totally ruined my digital camera. The rain just went through the zip. The replacement camera was treated to an aquapac a totally waterproof/underwater light bag which totally protects it against water. I need another one for my camcorder now because there is no way I am risking damaging it on the water rides (which you get soaked on) or in the torrential downpours I am expecting.
I have always carried a bag around with me, no problem. I think my family think I am a carthorse sometimes as I always seem to get lumbered with stuff. This year I wanted to just stroll around with perhaps just my camera around my neck but then when I thought I had my camera, camcorder, tickets, water, suncream, sunglasses, it quickly became clear I would need another bag again. So I am on the look out for a small neat backpack.