Thank you for your question. The quick answer is that there is no goat, real or otherwise, in Masonic ritual.
The origin and history of the Masonic Goat is still being discussed by Masonic scholars. A Web search on the term, "history masonic goat" (without the quotes) will give you more reading on the subject than you could ever finish. Basically, it appears that the Masonic goat was simply a joke that caught on and continues to be perpetuated today, mostly by Freemasons who continue to find it funny.
There is, apparently, some evidence that the Odd Fellows and the Elks did use a goat as part of their initiation ritual. Over time this peculiar practice came to be associated with all secret societies. The phrase "Riding the goat," came to be synonymous with being initiated.
Today, candidates may still be teased about riding the goat prior to their initiation. While I can't say for certain that some fun-loving Brothers won't have a candidate ride a goat as a ruse, I can assure you that it is not a part of the Freemasonry rituals.