You look in a horse's mouth to determine its age and/or health. So if someone gives you a horse, and you look in it's mouth, it's like looking for a price tag. It's rude!
Quintus: Thanks dude. Hey, look, the seam has really cheap thread.
Lucius: Noli equi dentes inspicere donati.
Lucius: It's Latin. Don't look a gift horse in the mouth.
Quintus. Oh yah, right. Mea culpa.
You don't want to know what it eats.
The modern interpretation is corrupted from the original 'given,' not 'gifted.'
To not examine a gift is to ignore subtle compliments or insults, and can be dangerous. Such was the case in the Trojan Horse.
"Don't look a gift horse in the mouth." quipped Martha.
"My girlfriend's taking me out, but I think she got the money from whoring at the truck stop," said Jose.
"Don't look a gift horse in the mouth," cautioned Miguel.
(On a chairlift) "Isn't it sad there are no tee pees or buffalo here?" wondered Jane.
"Don't look a gift horse in the mouth," snapped Stacie.