During the last battle in The Hobbit: The Battle of the Five Armies there is a scene where about 4 mountain goats appear, ridden by Thorin, Dwalin, Fili and Kili.
Where did these animals come from? I still wonder how this happens as I have never read any of the books.
It likely got cut.
From the trailer, at 1m22s we see a whole army/battalion of mounted goats.
But in the movie, when the Lord of the Iron Hills' Dwarf Army shows up, they are purely unmounted infantry. Only Durin is mounted on a Warthog (Warhog). If you squint at 3m19, you can make out four others that may be mounted as well, likely the generals for four battalions, when the forward Infantry breaks off to meet the newly arrived Orc Army.
The goats that Thorin and co use to attack the Orc commander do come out of nowhere as far as we know. It's commonly mentioned online as not being shown on screen before hand. Either it's corrected in the dvd extended edition, or never made it past the cutting room floor.
If the four blurry generals were riding something, then we can assume those are the ones that Thorin took. Or the goats were kept back from the main battlefield. Logically, an army will need support, and mounts are perfect for carrying large amounts of support material, healing supplies, arms, tents, etc. They may have been over the hill until called.
In the books, the Dwarves are not described as having goat mounts. It's purely a (neat and logical) movie addition. The entire fight sequence was changed.
Further to the answer @cde has already given, in The Hobbit: The Battle of the Five Armies extended edition Bluray the scene with the Dwarven Goat mounted Cavalry is included.
It is at about 2m50s into this YouTube clip that some goats are shown, then the entire mounted unit of Dwarven Goat cavalry attacks.
