I don’t know you but it seems to me you’re looking for an excuse to trim your beard or cut it off chas vesholom. Dogs don’t look at you, they smell you and hear you. They can hear your heartbeat and your organs churning around and they can smell what you had for dinner last night. Their eyes are way down the list.
There’s no easy answer to this depending where you live. I live in the western US and I carry a sidearm all the time. There’s no question how I handle it. In places like NYC you can’t do that and you usually wind up being sued or possibly arrested. Your life comes first. Larger members of the terrier/mastiff breeds such as pit bulls, American staffordshire terriers, bull mastiffs, American bulldogs not the English ones, Italian mastiffs etc. are fully capable of killing people and breaking any bone in a human body because of their jaw strength. Sorry for the graphic discussion but you asked and heres your answer. Dogs like Dobermans, German Shepherds and Rottweilers and Boxers can do a lot of damage but are less likely to result in fatality. All this doesn’t mean much if you don’t know dogs, but if you do it can help a teeny bit how you react to various situations.
There is no good way to deal with a bad dog. The dog might be rabid or it might be misinterpreting something or it could be a hundred different things. Do not smile at any strange dog or make eye contact. Do not run! The slowest dog on earth is faster than you and even a tiny little yapping chihuahua has sharp teeth if you don’t put your boot down his throat first. Walk away as calmly and nonchalantly as you can. Call the sheriff or police or if the owner shows up and gets the dog on a leash tell him you’re going to file a complaint for him letting his dog run loose. Then file it.
This is serious stuff dangerous and possibly life threatening. A big bad dog running loose is nothing to joke about.
As far as your beard goes I have a pretty long red beard and I’m a big guy and I’ve had my share of meetings with bad dogs bad bears and bad people. Try to stay calm and remember HKBH is running the world and animals and every thing else is totally under His control. Daven and work on your bitachon. That is worth more than anything.