Looking at a real horse's teeth shows how worn down they are over age. Looking at a horses teeth is to check its age.
The idiom could be modernized to: 'dont check the odometer of a gift car'
The idiom could be modernized to: 'dont check the odometer of a gift car'
In the case of other "gifts" the value can be negative. The trojan horse, software, and blankets from Lord Jeffery Amherst all need careful examination.