We put some goats in a fenced enclosure in Oregon -California mountains on the National Forest in late 1970s.  We came back hoping the Ceanothus brush would be eaten down, and the fence was broken down by bear we think and goats were gone, no signs of them.  I have since learned that a donkey is a big deterrent and will help protect goats.  As long as there is plenty to eat, the goats will probably not turn to damaging and stripping the larger trees, but smaller ones may be eaten.  They need to be moved before vegetative food becomes too scarce, or tree damage is likely.  I dont have any publications to share, but you may find something on internet such as silvi-pastture topic.

I know study done in goats reared in a dry forest from northern Peru where it is pointed  that primary productivity and forest architecture are important to goats raising: Uhlenborck & Rodriguez. 2005. EVALUACIÓN DE LA PRODUCTIVIDAD PRIMARIA NETA ARBÓREA POTENCIAL Y LA ARQUITECTURA VEGETAL PARA UNA MEJOR

PRODUCCIÓN CAPRINA EN EL DEPARTAMENTO DE PIURA. Zonas aridas 9:161-183.   

http://www.lamolina.edu.pe/zonasaridas/pdf/ZA09-Web.pdf

Currently a global meta-analysis on grazing effects in forest ecosystems is taking place. Check this link :-) http://www.eviem.se/en/projects/SR13-Forest-grazing/