Some of these pictures and descriptions may give away plot details that you might not want to know before watching the film.
This is based on the stories in "The Red Pony" by John Steinbeck, published in 1937. Some of the events in the movie have been changed from the book, but since Steinbeck also wrote the screenplay he must have approved of it. The movie retains most of the voilence and heartbreak and sadness of the book. It explores the relationships between a Central California rancher, his wife, her elderly father, and a cowboy ranch hand, but the core of the story deals with a young boy, Tom, who is given a colt that he falls in love with, but then it gets sick, with tragic results.
The snake scene is brief, but it's meant to show the juvenile side of Tom, who is maturing out of catching small animals to take home and into caring for his own horse. It also shows that Tom is a typical young country boy who loves animals but acts without thinking and needs discipline.
Tom carries a metal bucket to school that he uses as a lunch box. One afternoon after school we see him toss it through an open kitchen window into the sink. His mother, Alice, picks it up and opens it and is disgusted to see a frog and a snake inside it. She takes the lunch box outside and when she returns it's empty, so we can assume that she dumped the animals outside. She tells Tom not to put any more living things in the lunch box or he won't get any more lunch. She's tired of having to boil it out every day to sterilize it.
The scene comes from the story "The Promise" in which the boy (named Jody, not Tom) walks home from school, catches a horny-toad on the road, and puts it in his lunch pail. Then he captures "...two more horny-toads, four little grass lizards, a blue snake, sixteen yellow-winged grasshoppers and a brown damp newt from under a rock." When he gets home he throws his lunch pail on the kitchen sink and walks away. He hears his mother open the lunch pail and call to him angrily, but he doesn't go back in the kitchen, he goes to talk to his father who tells him that when their mare gives birth in a year, he can have her colt. Jody is overjoyed with the news. After that, his mother makes him promise not to fill his lunch pail with "...slimy, suffocated reptiles and bugs...." Jody is not worried about that because he suddenly feels that he is "...far too grown up ever to put horny-toads in his lunch pail any more." It works much better in the book because the movie has to combine several stories, concentrating on the red pony, not the mare's colt.
Alice calls it a toad, but what we see in the lunch box is a Bullfrog (and we hear the sound of a Pacific Treefrog). We also see a small Green Snake, a genus that is not native to Salinas, California, where the book is set, and is found only east of the Rocky Mountains.