There are a lot of different possible symbols throughout this story. The main one, of course, is the rocking-horse itself; it symbolizes the love that Paul wishes he had from his mother. It symbolizes his fruitless search for her affection. A rocking-horse is not real; it can never actually transport Paul, just as getting money can never actually give his mother happiness, or Paul her love. It is just a fake, plastic toy, just as money is a fake reassurance of love and happiness. So that is the main symbol in the story, and the most powerful one.
Another symbol could be the whispering in the house; it is a representation of how greed is never satisfied, and always demanding. The more money they got, the louder the whispers were. They were never quiet, as long as money and wealth were the focus.
Irony exists in the fact that Paul actually does win money from riding the horse; that is totally unexpected. Also, it exists in the fact that once the mother has money, even after living without it for a while, she does not use it wisely and soon runs out again. Then, the ending--for the first time the mother has shown actual concern and love for Paul, and that is when he dies. It is a very sad story, and one that can teach valuable lessons about what is truly meaningful in life. I hope that helped; good luck!