I would not trust wood-slat snow fence to keep predators out, they can bust apart hte slats if they want, and it would only hold goats in if they chose not to whack into it too hard with their heads. (Dunno bout goats, maybe it'd be ok that way, but sure would not hold for sheep)
I am using it behind my cattle panels to keep in the kid goats. They were crawling right through the cattle panels. I am finding the combination of the two to be pretty secure so far LOL
4 feet is a pretty good hieght for most goats, Your bigger problem with the snow fencing is it holding up, if they start scratching on it all the time, or you use it to divide two pens and they bang in to it. But I am nerver against trying. A couple satisfied laid back goats, would probably be fine, If you have a problem with stray dogs, they may chew it down, to get into your goats.