We have some springs that just "leak" out of the ground and go down this hill. We have thought about digging a hole just below where it leaks out of the hillside and putting a kiddie pool in it to let the water flow into that and fill it, when it fills the kiddie pool it would just overflow back down the hill. Do you think the deer would go to this buried pool to drink?
The other thing with your small plastic pool, would be to put a weighted stick (on one end) that has one end sticking out of the pool and sitting on the soil near by. The reason for that, is if any small critters get in there, they have a way to climb out. Don't want to have any small dead critters spoiling your pool.