Let's say I have a Bard that has learned the Find Steed spell and Simulacrum through the Magical Secrets trait.

Find Steed (and Find Greater Steed(XGtE 156)) both specify the following (with slight differences):

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

If I'm mounted on such a steed and were to cast Simulacrum, targeting myself, can I choose to also target the Steed, and if so, what happens?