No, this will not work
When you cast a spell that targets only one creature and doesn’t have
a range of self, you can spend a number of sorcery points equal to the
spell’s level to target a second creature in range with the same spell
(1 sorcery point if the spell is a cantrip). (PHB)
So, when you use Twinned Spell you are targeting an additional creature thus conflicting with the one target restriction for that effect in Find Steed:
...you can make any spell you cast that targets only you also
target your steed (PHB)
The same is true in the reverse case as well; using the spell sharing feature of Find Steed also results in multiple targets thus making it invalid for use with Twinned Spell.
Jeremy Crawford seems to support this as well in his description of Twinned Spell:
[Twinned Spell] lets you add another target to a spell but only if that spell on its own can target only one creature and it's also not a spell that has a range of self. (Dragon Talk 1/19/17 20:40)
Jeremy Crawford made an almost identical ruling for the case of split enchantment (a wizard enchantment ability)
Split Enchantment and Twinned Spell are mutually exclusive. When you use one of them, the spell no longer targets only one creature.
Split enchantment says:
...when you cast an enchantment spell of 1st level or higher that targets only one creature, you can have it target a second creature.
This is an almost identical case to the case of Find Steed and Twinned spell. Thus the ruling absolutely applies here as well.
Both of these Spells change a one target spell into a spell that targets two creatures. No matter how you cut it, after using either of these abilities, you now have a spell that is targeting more than one creature. Thus is ineligible. It very clearly no longer "targets only you" or "targets only one creature".