How does the Misty Step spell interact with a mount?

Question

While riding a mount, would you be able to cast misty step and have the mount teleport with you? Or would the mount be left where you cast the spell?

And, if it was used with a mount from find greater steed, would that change the result?

Answer 1

A mundane mount would not be teleported with you

Misty step has a range of self which means it affects only the caster.

Briefly surrounded by silvery mist, you teleport up to 30 feet to an unoccupied space that you can see.

It also has no text allowing for additional creatures to come along with you. The caster and the horse are separate creatures. Thus, the horse would not get affected by the spell.

Compare this to dimension door which says:

You can also bring one willing creature of your size or smaller [...]

Dimension door allows you to bring other creatures, but misty step does not have the same or similar text so it does not. (Side note: dimension door would also not work on teleporting a steed because it is bigger than you.)

If your mount is from find steed or find greater steed, then it will be teleported as well

If your steed was summoned using find steed or find greater steed, then misty step would affect them because the spell specifically says:

While mounted on [your summoned mount], you can make any spell that targets only you also target the mount.

Of course again this is only specific to steeds created by these two spells.

Answer 2

The mount would be unaffected

Misty step only teleport you, so the mount would be left behind (emphasis mine)

Briefly surrounded by silvery mist, you teleport up to 30 feet to an unoccupied space that you can see.

Find steed

The find steed paladin spell creates a special mount that could be affected:

While mounted on your steed, you can make any spell you cast that targets only you also target your steed.