水遊びって英語でなんて言うの？

Wade = to walk through, or in to, a body of water (ocean, lake, pool). You get part of your body wet but, you are not actually swimming. You can be just walking or standing (to cool off) or playing in with toy balls, boats, etc.

Playing in the water is for pleasure, we swim or play with a ball. We do get water sports as well, like snorkeling, rowing, water polo, jet skiing and sailing.

1. With very young children especially at nursery school, 'water play' is understood to be good for children's development.
2. If you horse around or horse about, you play roughly and rather carelessly, so that you could hurt someone or damage something.
   "Later that day I was horsing around with Katie when she accidentally stuck her finger in my eye."
   3.Splashing = causing (liquid) to strike or fall on something in irregular drops.
   "She splashed cold water onto her face"

The act of playing in the water is called swimming or paddling.

I paddled in the shallow water.

We went swimming in the pool.

The children paddled in the cool water of the stream.

We swam in the water of the ocean.

Waterplay (noun)
This word refers to all forms of playing with water.

Examples
Marco Polo
Water balloon fight
Water gun fights
Swimming races
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Example
A: What is your favorite thing about summer?
B: Waterplaying. It is so much fun.

Marco Polo is a very common game with young children to play in the pool, its like hide and seek using sound not your sight.
Swimming is the act of playing in water.
A general term for playing with water is water games or paddling, e.g. my daughter loves paddling at the beach.

Playing in water.
Playing with water.
Splashing around.

Are all acceptable to describe this situation.