The state of mind during zazen is described as "dropping all thought." I have come to find that if one can "drop all breathing," it is much easier to drop all thoughts, desires, etc... and be in the present moment during zazen.
Don't try to inhale or exhale, just stop breathing, sit with no breath for a few moments, and when you are ready to take a breath your body will do so. Its suprising to see how much "extra" breathing we actually do in a day.
Even though the Soto sect does not focus on counting breaths, and focuses more on simply sitting in the moment, it seems to me that we can learn alot by observing breath in a non-judgmental way (but, of course, not to the exclusion of our environment).