My 3 months old yorkie definitely has an attitude! Small dog, BIG attitude

He loves attention and loves playing with us, but I have been noticing he gets somewhat aggressive? Or maybe just playful, but its hard to tell. While playing tag of war (his favorite) if I grab him or he doesn't really get his way he gets snappy. If it gets out of control I stop him and tell him to calm down. I'm never mean to him, but do use firm voice. My boyfriend likes to play with him but "getting down to his level" and he goes crazy jumping at his head, biting his hair and trying to bite his face! When he gets too playful he bites his nose, (doesn't do that to me), are those type of games not a good idea?