The Simulacrum spell targets your Steed, but it won't copy it
The spells Find Steed (and Find Greater Steed) both will allow you to target your steed as well as yourself with Simulacrum. However, the spell Simulacrum states (PHB, p. 276):
You shape an illusory duplicate of one beast or humanoid that is within range for the entire casting time of the spell.
However, even if your steed appeared to be a beast (e.g. if it was in the form of a Warhorse), according to the text of Find Steed (PHB p. 240, bold added):
The steed has the statistics of the chosen form, though it is a celestial, fey, or fiend (your choice).
So although you could target your steed with the Simulacrum spell, the steed is not a valid target of the spell by virtue of its creature type. And according to an (optional) rule in Xanathar's Guide to Everything (p. 85-86):
Invalid Spell Targets A spell specifies what a caster can target with it: any type of creature, a creature of a certain type (humanoid or beast for instance)... But what happens if a spell targets something that isn't a valid target? For example, someone might cast charm person on a creature believed to be a humanoid, not knowing that the target is in fact a vampire.
If you cast a spell on someone or something that can’t be affected by the spell, nothing happens to that target.
The example above demonstrates that the ability to target a creature with a spell does not automatically make the spell's effects apply to it. Just as you can target a vampire with charm person (which wouldn't do anything to the vampire), you can target a fey, celestial, or fiend with Simulacrum, but it won't do anything.
So although Simulacrum will both target you and your steed, it will only duplicate you, not your steed.
Of course, the Simulacrum copy of you could cast Find Steed itself, and gain a steed of its own. But this would cost a non-recharging 2nd level spell slot. Otherwise, the copy will have to resign itself to a steedless existence.