If you're so stingy that you can't stand to spend any money, not even to buy your adorable little cousin an ice cream cone, you are closefisted.
People who prefer to hang onto their money are closefisted, especially if they aren't generous to others. You might also describe them as penny-pinching or call them tightwads. All of these terms provide clear images of hands clutching money tightly inside them — closefisted came first, around 1800, and tightwad followed about a hundred years later. The opposite of being closefisted, fittingly, is to be openhanded.