It really depends on the extent of the bark damage. If they are older vines and the goats pulled off some exfoliating outer bark, then there will probably be no negative effects. But if they stripped and chewed into the growing layer, especially on young plants, the conductive tissue could be damaged or exposed to sunburn and fungal infection, and uptake of water and nutrients compromised. The more of the circumference affected, the more damage and negative effects can be expected.
If you are not sure how deep or extensive the damage is, then it's wait and see. Wilting of foliage would be a first sign of extensive damage, followed by dieback of sections or the entire plant.
Keep the goats away from doing more damage of course. Water and fertilize to ensure best conditions for recovery.