You can tell a horse's age by the state of its teeth. Thus, if the gift-giver saw you looking into his present's - ie the horse's - mouth, he would think you most ungrateful! A present is a present, in other words, so just accept it. 'Seize the opportunity' is another way to interpret the saying.
As my colleague advises, you can tell a horse's age and physical conditiob by checking its teeth, and this is a common check made by potential buyers looking at a horse. If yours is a 'gift' horse, you would appear very rude to be checking if it is healthy or not, so the phrase has come to mean that you do not receive a gift or an oppurtunity with bad grace - accept gratefully.
Hello, i think it's got something more to do with greek legend and troy, can't really remember but basically some warrior-types wanted to attack but using the element of surprise so they pretended to be giving their enemy a big present - a humungous horse. however inside the horse was all the soldiers and once they were in they all got out an killed everyone. although you'd think that the expression would be DO look a gift horse in the mouth (jn case there are soldiers hiding in it). sorry, not much help after all.