I first want to say PLEASE NEVER HUG A STRANGE DOG. Although it is very tempting to give a cute dog a big squeeze; in dog terms it is very rude and may get you into a heap of trouble.
We all love to pet our dogs; it's actually good for us, lowering our blood pressure simply by touching them. But what if your dog doesn't like to be touched? A touchy situation for sure; you got a dog to keep you company and now you discover that they are not the touchy feely type, great. There are many different types of reactions to touch; some love it, like my Luke. Others thinks it's sort of nice; there are the dogs who accept it; only barely tolerating it. And then there are the dogs who do not want to be touched; some will move away while others may let you know with a growl that your touch is not welcome.
Most family pets that don't like to be touched simply pull away. If your dog growls at your touch you are probably dealing with leadership issues and need to have a professional have a look at your relationship. If your dog just doesn't like to hug and kiss; rest assured, there is hope. Tilley is not a touchy feely type gal; that is if we approach her and give her a big hug. But she loves to come up on the couch and snuggle up beside you; even lay in your lap.
It's all about what our body language means; and a hug in dog terms is a dominant gesture. It is the equivalent to being mounted. Never considered this before? And if we dissect the hug even further; a hug coming from below will be accepted far more easily than coming from above. If I hug Tilley from underneath her stomach she is fine with it; she doesn't lean into it like Luke but accepts it. If I hug her from above and around her neck or chest; I can feel her pull away.
Positive; positive, positive. This is the way to go to teach our dogs that touch is not only good; but great. Start slowly; and always "quit while you are ahead." A quick touch is much easier to accept than a half our petting session. So start small and work your way up. Add treats to the touch game. A hand on your dogs neck as you give them a yummy treat; a treat offered while you rub their chest.
Some dogs are over stimulated by touch; so for those types you want to keep it short and sweet. And touch can also be a status seeking behavior; bet you never thought of that before. With my boy Luke; it is often status seeking with strangers. When someone new comes into our house and lavishes attention and petting on Luke; "that's right; who's the boss?" When they think they are the best of friends; they go to move into the living room as Luke lunges at them barking. The person is left thinking "what the heck is wrong with this dog?" When this is normal procedure with Luke; he established who was the top dog as soon as the lowly human started the petting procedure. Now the human thinks that they can just simply walk about "his" house?
The best way to enter a home with a dog is to ignore the dog. Ignoring solves so many issues; over excitement, over submissiveness, fear and status seeking behaviors. Then once you are in the house; you can acknowledge the dog. But keep it simple and watch for acceptance of touch. Don't assume anything with dogs; they are all different and have their different needs for space.
For many dogs; learning to love our touch is a process. We cannot force it upon them; we must teach them that it is a wonderful and mutually beneficial activity. If after all your work they still aren't on board; then that is who your dog is, they need their space. We should respect that.