Is it natural for my breathing to slow down during meditation?
Yes, it is common for the breath to slow down or even pause for a while during meditation.
There is a great natural principle at work here. It is why pranayama is so effective for cultivating the nervous system. Recall that "pranayama" means "restraint of the life force". When we restrain the life force in a simple unforced way, something is created. The gentle restraint of breath creates a biological vacuum effect, a small suction on the life force in us. The body must deal with this gentle deficit of life force in some way. It does so by pulling from the vast storehouse of prana within the body, and this prana flows out from deep within the nervous system. This is a new dynamic in the nervous system, and the outflow of prana from within plays on the nerves with a great loosening and purifying effect. This process is at the heart of all the effects that come up from pranayama. Right behind the flow of prana coming up in pranayama is the bounteous flow of pure bliss consciousness, assuming we are practicing our meditation every day.