Could I, as a paladin mounted on a mount summoned as per the Find Steed spell, cast Warding Bond so that I am granted the +1 to AC & Saving Throws and so that I get the resistance to damage and the mount takes the other half?
Warding bond is touch range, touch ranged spells are allowed to target self:
Some spells can target only a creature (including you) that you touch.
Find Steed then states:
While mounted on your steed, you can make any spell you cast that targets only you also target your steed.
Warding bond then states:
This spell wards a willing creature you touch and creates a mystic connection between you and the target until the spell ends. While the target is within 60 feet of you, it gains a +1 bonus to AC and saving throws, and it has resistance to all damage. Also, each time it takes damage, you take the same amount of damage.
This thread is similar and concerns the same question using a familiar instead: Can I use my familiar to cast Warding Bond on myself?