The fact that you cannot snore and dream at the same time is well-circulated. But, there are also a number of sceptics who are diehard believers of ‘you can snore and dream at the same time’ idea. They provide extremely valid points too. However, both sides are at a disadvantage as there is no official source that states whether you can or cannot snore while dreaming and vice-versa.
The sceptics believe that snoring and dreaming are two separate entities. Snoring happens when the muscles of the mouth and throat relax. This relaxation causes the soft palate of the throat to sag in relaxation.
Since we still intake air, the air passing through the airway causes the narrowed airway to vibrate. This is how the sound of snoring is made. The narrower your airway, the louder your snoring is. This can be a sign of sleep apnoea.
So, if you are disturbing others when you sleep because of your snoring, you may want to consult a doctor. However, there are no conclusive results on the subject still, and both snoring and dreaming are kind of unexplored territories.