This is confirmed to happen to all ponies when the helmet is taken off. The mane reappears when changing rooms, for obvious reasons (the model is reloaded), but this is very consistent.

In T88#18511, @Rattletrap wrote:

Currently, the helmet works for foal models. It does not work for filly models

I would like to also add the speculation that this bug is heavily connected to the reason why the flower bushes fling you into the air, and why other places with sharp geometries do the same.

Oh, foal armor is never visible for me. At all.

UPDATE: At least one of these trees is in Ponydale, and there are countless ones in the Heartlands.

Oh, and I didn't report the teleportation glitch near the burnt-out area, mostly because I have not been able to reproduce it, and I have no idea exactly how it happened.

Interestingly, when I jumped onto the sign in Cantermore, it teleported me to the Crystal Kingdom. The sign there put up the menu when I teleported into it (hoping to get teleported again).

Yep. Reproduced on Linux 64-bit.

Additional Update!

Update: This still needs to be fixed, as many users with different Linux distributions will have issues, but reinstalling my OS and upgrading to Ubuntu 16.10 (from 16.04) solved the issue.

Same here.

Update: the other armor pieces also disappear, but still give protection.

My initial response was misinformed. I know that those starter moves are supposed to be the same for every race.