Hi Tammy first of all i would not worry to much, horses chew bark even feral horses there are many good resons why heres afew,
1/ young horse do it to loosen milk teeth and strengthen gums.
2/ bark is a natural fiber which horses need .
3/ In spring the new grass is plenty full but has less fiber than is needed if just on grass.
4/Horses have a phyicologicol need to chew and fiber is very important to them and their gut
If you put old apple tree logs in the feild and maybe some in his box
he can chew safely on those and you need not worry.