"To eat like a horse" can also refer to a vegetarian.
"To work like a horse" is usually stated as "to work like a mule."
'Don't look a gift-horse in the face.' This is actually "Do not look a gift- horse in the mouth." You can tell the age and condition of a horse by "mouthing" it. That is by checking the wear and tear on its teeth. You do this to determine if you wish to pay the asking price or bargain down or pass on the purchase altogether. After looking into the horses mouth, you may reject the horse completely.
If someone gives you a gift, be appreciative, do not be ungrateful, do not be critical, after all, it is a gift. You are not purchasing the item so you have no right to complain about it.
But you missed the most common one - "hung like a donkey." This is directly from the Bible. It means a male who is well endowed.