I know it causes respiratory problems with chickens. The goat house is made of painted chip board, they've chewed alot of that off, I can't imagine pine or cedar bedding would be harmful.
No red cedar! No oak or any other wood shavings with high tannin levels. Straw is propably best for goats. They like to try and chew on everthing anyway. So bed them on something that won't make them sick if they eat it.
No matter what you put down it will end up covered in wasted hay.. I have used straw.. that is such a pain literally and figeuratively to clean up.. I now use pine shavings and have not had a problem.. I have my own supply of pine boards and a planer to make my own shavings now.. i was purchasing from feed stores by the compact bale of shavings.. much cheaper my way.