The nose is involved even without retrohaling, and I've never seen anyone smoking with their nose pinched shut. Hence, it's involved - even for those who don't purposefully "snork".
That being said, it took me some while before I could actively retrohale, and the concentrated action does change the perception for me; sometimes appreciated more, sometimes less.
This, along with some that others said.
Even if you don't retrohale or blow out your nose, flavors do creep up into the back of your nose, it's unavoidable unless you completely close off the nasopharynx, which you can't really do. This is a well known scientific fact about taste perception:
en.wikipedia.org
Retrohaling is just purposely pumping the smoke up in this area to varying degrees to get stronger and more concentrated retronasal scents than you'd otherwise get with the smoke sitting just in your mouth. And it doesn't have to come out of the nose, you can pipe some smoke in and blow out both the mouth and nose, or can pipe in a lot, or blow completely out the nose. But even without retrohale, some of those volatile scent compounds WILL go up into the back of your nose, even if the smoke itself doesn't (or doesn't much).
Pinching your nose shut deadens, but doesn't eliminate, flavor. The effect is probably similar to sticking a straw in a liquid and then capping the end with your finger, when you lift out the straw, liquid stays in until you release your finger, then it falls out.