Lots of owners feed fully aware "live" prey. Many snakes will refuse prey that doesn't move.

This is a good way to injure your snake, it definitely depends on the species and the individual temperament of the snake, but there are ways to entice a snake to eat dead mice (you can warm them, and wiggle them).

It helps to understand how snakes detect and catch prey.

And this is considered really creepy and weird by many people.