Ours drink out of a pond sometimes, but they don't try to walk in it. Chicken's feathers get water-logged and it will weigh them down, drowning them. I wouldn't go anymore than six inches, unless you have bantams, then have even less.
My full grown chickens will walk through water but not really play in it. I wouldn't put any pools around chicks because the can drowned being young, uncoordinated and stupid. They can also get all wet and that could chill them to death.
SIDE NOTE: Its common with raising chicks to put marbles (I have used small pebbles) in the full sized water'ers (fountains) to prevent problems. After they are a couple weeks old that isn't really all that necessary.
If you want something for them to play on I would suggest making small perches.
I have a water bucket (old horse feeder) that I keep filled about 4 inches. Many of my hens love to step into it and not just when they are drinking. Since I live in Arizona and it is really dry, l like to have it available to help keep their feet from drying out. When I have little ones hatch out, I put it up high enough so that they do not have access until they are older.