Snorkel-breathing

The issue might be your stroke rate and breathing cycle without the snorkel. 

If your stroke rate is low and you breath on every other stroke as most people do, you might simply not be getting enough air to feel comfortable in the water at moderate efforts. This is because your swim-specific muscular endurance in your arms are too weak to keep up a faster stroke rate and thus the problem is compounded when you breath on every other stroke, but solved when you put on a snorkel thus allowing you to breath whenever you want. 

I had this same problem for quite awhile as a beginning swimmer as well. It wasn't head position that fixed it for me - it was getting (substantially) stronger in the water so I could maintain a much faster stroke rate over distance, thus allowing me to take more breaths more frequently. This is a big reason why swimming is so hard and uncomfortable for newer and slower swimmers - the uncomfortable feeling of lacking enough air due to the slow stroke rate makes it unpleasant. 

Ironically, now that I'm decent enough in the water, I get significantly more air without the snorkel and thus swim faster without it.