grazer

from The Collaborative International Dictionary of English v.0.48

Grazer \Graz"er\, n.
   One that grazes; a creature which feeds on growing grass or
   herbage.
   [1913 Webster]

         The cackling goose,
         Close grazer, finds wherewith to ease her want. --J.
                                                  Philips.
   [1913 Webster]