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?
Best Answer
No
You run into several problems trying to cast Warding Bond on yourself and have your steed take the damage. You seem to be able to cast warding bond on yourself (which seems fine, you get +1 AC take half damage but then take the damage twice). The target of the spell is the one who gets the AC and the resistance, the caster of the spell is the one who takes the damage. Find steed does not make your horse the caster of the spell therefore you cast it on yourself and your horse and you both get the benefits while you take all the extra damage. Additionally I'm not sure how a horse could wear a ring but (assuming you can get a ring on a horse) you would most likely need three rings (2 for yourself and 1 for the horse).