Stoats eat rabbits, mice, voles and so on. Haven’t come across any accounts of them eating snakes, but its possible. BBC Wildlife did a David Attenborough documentary on them called “Stoats in the Priory”. It is worth getting hold of to see diminutive stoats killing and dragging rabbits more than three times their size and weight back to their young!
And yes, stoats are weasels. Their North American subspecies is called the short-tailed weasel, or in northern regions where it undergoes winter whitening, the ermine.