Hello,
No one can change the cosmetic looking. Neither choose the companion or the mounting.
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Observed the same issue, which is especially annoying, as playing without a pet is really some usability downgrade…
There was no wardrobe change mentioned in The 2.3.0 PTR: What You Need to Know — Diablo IV — Blizzard News, not even remotely, so why is it broken…?! 
No cosmetics can be equipped currently.
Not even that our cosmetics were not imported.
But Just salvaged some and the additional looks do not show up in the screen to apply them.
Also can’t equip anything else in the wardrobe screen, like pets, mounts.
Mount works from mount key, I went to the stable, not sure if I needed to, but not sure how to call my pet outside of that.
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