Yes, dog tail wagging is involuntary. In other words it is a reflex, instinctive action over which the dog does not have control or has no desire to control. In fact domestic dogs don’t even think that they are tail-wagging as it is that instinctive. This is my considered opinion.
It is also worth mentioning that tail wagging is not necessarily an expression of happiness. A dog might be happy but the behaviour is a physical expression of a mind that is slightly conflicted between wanting to be somewhere and being frightened to be there. I’m sure that the degree of desire to be in a certain place outweighs the fear of being there for tail-wagging dogs but there’s an underlying anxiety which creates a conflict and that conflict is made manifest in a physical action.
It is difficult for a dog owner to accept because they want to believe that their dog has nothing but love for them but humans tower over their dogs and are dominant to them. If a dog wants to be with their human companion after being separated for a while they’ll approach and be with them but there may be a little bit of apprehension in their minds at the same time. This causes the tale-wagging.
Another reason why a dog wags her tail is because it creates an odour signal. The tail wagging described above is a visual signal but in this instance vigourous tail wagging movements have the effect of squeezing their anal glands which emit an odour: anal scents.
Humans can’t detect the smell but they have a significance for the animals themselves. This is an added benefit or bonus for the dog. Confident dogs wag their tails in an upright position.
Tail wagging can be observed in wolves when they encounter one another in a range of social context. It is often misunderstood by people as only a sign of friendliness. This is because people see it when dogs meet their human companions or dogs with whom they are friendly.