Are the plants in the ground? If so, it could be rabbits or even curious crows. If you have neither of these pests and the plants are in containers or a window box and out of reach for rabbits than look for small green worms or moth larvae. These insects will hide under leaves or even in the soil and using a flashlight at night may be the best way to catch the culprit in the act. The good news is that the plants will become less tasty as they mature and Rosemary is one herb that is not appealing to most pests once it grows.  Do not overwater as Rosemary is a sun and heat loving plant that resents soil kept moist. Warmer weather is ahead and I predict this problem will soon be outgrown even if you do nothing. Keep growing, Marianne Binetti