Sheep follow.
Goats must be driven.
I raised milk goats for eighteen years.
They wore collars but when you but a rope on them you could not drag them.
I learned that when I put a rope around their rump, below their tail and routed the two ends through their collar, then I could pull them. But....in reality it wasn't a pull, it was a push.
Goats won't eat anything(everthing). That's a myth. They are very picky eaters. When their hay falls on the ground, they won't eat it, since they are very susceptible to parasites. I had to make 'keyhole' feeders for them so that they would have to rear up, put their head through a round hole, then drop down to eat the hay with their neck in a slot. To leave the feeder they had to reverse the procedure. This kept them from dragging the hay out of the feeder, and on to the ground.
Goats are lovely animals however. Nice to have around.
The LORD uses sheep and goats as an analogy, comparing those who willing follow Him, versus those who resist.
Mat 25:31-46 is concerned with the second coming of the LORD Jesus to earth at the end of the tribulation. It is then that He will sit on His glorious throne, the throne of David, to establish His Kingdom over Israel and to the ends of the earth. In these verses there is a third group which are neither sheep nor goats. They are Jesus' kindred of the flesh, believing Jews who survive the Tribulation(Jacob's trouble). During the Tribulation, the Beast will be doing everything he can to destroy the Jews(Rev 12:17). Any Gentiles who seek to help the Jews during this time will be placing their own lives in jeopardy, but it will also mean that they have become believers in Jesus Messiah during this time. Their blessing and helping the Jew during this time will reveal that they are believers.
Thus, they will enter the Messianic Kingdom, while those who didn't believe and aid the LORD's Jewish brethren will not.
These verses are not about entering heaven. They are about heaven coming to reign on earth through Jesus, the promised Messianic King.