A few things that are apparently lost on this. Goats produce methane. Methane is a way more powerful greenhouse gas than Carbon Dioxide. Goats also produce carbon dioxide from the grass, which would have otherwise have been converted to organic matter for dirt. So, the value of this is dubious.
Also, the Earth is actually very cold by normal standards. Everyone keeps talking about global warming, but even with it the Earth is relatively cool. I also haven't seen a study indicating the effects on plant life. Unless we keep knocking down forests and such, plants should benefit from the extra carbon, and can grow faster with it, providing a negative feedback mechanism. However, if we keep destroying their habitats, that complicates things. Methane, of course, is not used by plants though, so likely doesn't have a negative feedback loop. It's also responsible for about 25% of the global warming, despite being much less concentrated. It's just a much more effective greehouse gas.