At this point, you've got a horse that is reliably targeting and lowering his head, understanding that he's working for a click that will be followed by a treat.
BUT, you've also got a mouthy monster mugging you for treats!
Mugging for treats is never ok - not even in clicker training. This is where clicker training and "treat training" are very different. Treat training, without a click to mark the correct behavior, usually fails to communicate the idea of "earning" a treat through correct behavior. Rather, the horse just knows it does some stuff and eventually gets a treat shoved in its face. Clicker training "marks" the correct behavior with a click, allowing for accurate communication of the correct behavior, and then your horse MUST politely wait for his reward.
Have you ever tried telling a kindergartener what NOT to do, only to find out they did something else you didn't want them to do instead? It's much more effective to tell them what they SHOULD do instead to direct their behavior into being what you would like it to be. Horses are the same way. I have no problem giving my horse a firm smack on the nose for treat mugging. However, I also make a point of showing my horse what I DO expect from him - by clicker training it! In order for my horse to receive his treat, he must be politely waiting for it until I put it up to his lips. This is when it's ok for him to take it out of my hand, and never before that. If he reaches for a treat in my hand, I close my fingers around it and take it away. Moreover, if he starts mugging the treat back or is just not getting the message about what he should be doing, I focus specifically on this behavior: I start clicking when he turns his head away from the treats. Between the clicking, the awarding or witholding of treats, and the occasional smack on the nose, it didn't take long for Flash to learn to be a polite little pony and wait until I say he's allowed to take his treat.