Is my 6 month puppy food aggressive?

Lately, my 6 month old Labrador/Doberman mix puppy (male), has begun snapping at other dogs of all shapes, sizes, ages and genders whenever food is near. If I have a treat in my hand and another dog comes over to sniff it, he will turn around and snap. Also, he's always sniffing the ground looking for food or something to eat and if he finds something, and another dog comes over - he will snap at them. These are all dogs that he usually plays with very well. He's a very boisterous dog, and always takes the dominant position when playing. He's a rough-player but not seemingly aggressive - he will pin the other dog down and bite the neck (not aggressively and not enough to hurt the other dog. Today, he ran into a wooden post whilst playing with another dog and hurt himself and let out a big 'YELP!' this other dog came back to play with him, whilst Harley was just getting himself over the pain - and he jumped out and ran towards this dog with his teeth bared growling and snapping. Was this because of the pain or does he have an aggression issue? Also, is he possessive over food? I feed him well but he always looks for food.