He's a growing intact male that is starting to mature. Most people will tell you that this is something you're going to have to manage and you won't be able to train him to not do anything. The issue with "correcting" the growling/snarling is that he'll just stop growling/snarling and will just go for the bite when he's had too much.
Most of us with intact males do not let them interact with other males for a long time. I make sure to really watch my boy when he's around unknown dogs (like in a dog park setting) and make sure he doesn't start getting aggravated by other dogs. I'm actually very surprised that the day care allows your boy to go there, every single one around me only allows altered animals past the age of 6 months. Just because he gave the puppy the warning, doesn't make how he acted alright. I'm sure if damage was done, the puppy's owner wouldn't be as understanding about the situation.