Nostalrius Begins - Quality wow vanilla realm (1.12)

At the beginning of AV as you run out of the cave you are rudely dismounted.
This also occurs inside of Ironforge as you run through the corridors (maybe intended)

You are not supposed to be able to mount inside the spawn cave of AV - this is a bug and you're supposed to get dismounted.

As for IF, I do not know if it was like that in retail, it is simply too long ago, but I always recall being dismounted in the small corridor leading from the bank to The Forge.

"This also occurs inside of Ironforge as you run through the corridors (maybe intended)"
You shouldn't be dismounted unless you enter a building. However, even back in retail Classic, it was possible to be dismounted for touching their walls or going over their roofs. It was not scripted properly, even back then by Blizzard. The game was easily confused as to whether you were indoors(no mount), or outdoors(mount). The AV cave btw, is a no mount(indoor) area. If you're using it in there, that would be the problem. You're supposed to run out of the cave on foot to the snow, then mount up outside. Similarly, being inside a mine or tower is indoors.

Fixed.