If I had to guess, I'd bet your dog doesn't like the "bouncy" kids - the ones that are likely to startle him because he can't hear them coming. Our old Cattle Dog resorted to that tactic as he lost his hearing (sight, too) - and it's exactly why we finally put him down. Didn't trust him around the grandkids.
BUT - I'm not advocating putting your dog down. You're going to need a good trainer who can teach you and your dog hand signals; and someone who can assess if the dog is truly a biter, or can be convinced to be polite with some good training? Also - if the dog is nipping at heels/lower legs - that might be a herder "herding". That's easy enough to stop with a little bit of training - you're dealing with breeds that are super-smart!
On edit - I want to add that both Aussies and Border Collies (and probably many other herding/working breeds) are very people-oriented, and willingly look to their humans for commands. I guess I'm saying if you're going to work with a deaf dog - these breeds might be easier to retrain than a sled dog, for example. As my beloved Aussie Ike grew old, he lost his hearing, too - but he had good sight, so we invented some hand signals that worked for us, and he simply wandered around the yard, glancing at the door every 20 seconds or so, to see if I was there to wave him back inside.
You might also invest in a really good training collar - one that allows you to control the signal the dog receives? And then teach the dog to come to a vibration setting. I mean, unless you're going to always have the dog on a leash - you'll need to let it know you want it to come back to you. Or at least look at you so you can give it a signal by hand.
Lastly - if your dog has a lot of white on it - it's probably an Aussie.... people who don't know what they're doing will breed a merle female to a merle male; and quite often the pups of that cross are born with too much white, and are deaf :-(