My son (8mos) has had the snorty sounding breathing since shortly after birth. In fact, he got so bad, he was wheezing. You could feel it in his back when holding him.
Other than the snorty sounds, he's healthy. Eats well, weight is good, growth is good, nose isn't runny, eyes aren't red. He also was exclusively breast fed until 6 mos then we added food to the mix.
We had him on a nebulizer with albuterol and pulmicort, but nothing was helping. We took him to an ENT and a ped. pulmonologist. I really wanted to find out what was causing it. I alos have two children (daughter will be 4 in Aug) so I knew it wasn't normal which is what my ped. kept saying.
The ped. pulm. said it is most likely laryngomalacia and tracheomalacia. Basically, the trachea and larynx are "floppy" instead of rigid. Therefore, every time he breathes in the tubes collapse. It sounds alot worse than it is. It's not dangerous and he'll outgrow it (the tubes will "harden") by the time he is 18mos.
Without scoping my son, the pulm. couldn't make a definite diagnosis, but given that he is growing and interacting well, he really doesn't want to put him through a scope unless the symptoms don't go away by 18mos.
It sounds like your son may have the same thing. I recommend seeing a ped. pulm. I love the Dr. we went to. After being told over and over again that it was nothing, it was really reassuring to meet with him and have an answer to why my son was always snorting.