We need to remember that Doug's brother was the one who literally littered the school with pictures of Holling in his Ariel outfit dressed as a fairy. Therfore we know that Holling definitely would like a chance to get back at Doug's brother. He gets the perfect chance in January when it is very snowy and, one morning before school, he Holling sees Doug's brother and realises that he has the perfect chance to throw a snowball at him and then run off into school so that Doug's brother doesn't realise who threw it. Note how Holling imagines the scene:
In my mind I could see it all: I pull back my arm, plant my left foot, Doug Swieteck's brother comes sliding into sight, i release the fastball, his face turns toward me at the last moment, and the snow-ice-slush-spitball splatters against his nose. Perfect.
Even though Holling believes it is not going to happen like this, he still goes for it, and it satisfied when it all works out completely as he anticipated. Holling gets his revenge, and as he is studying Macbeth at the time, there is definite symmetry between his life and this play.