Horses are herbivores and only eat plant matter. They have multiple stomachs which allow them to digest cellulose that humans could not eat. Horses may occasionally swallow insects while they eat their grass, but this is not enough to classify the horse as a carnivore (a meat-eater) or even an omnivore, which is an animal which eats both plants and animals.
Also, many frogs are often poisonous. As a general rule, brighter colored animals are often poisonous for other animals to eat--this is Nature's way of telling predators to back off. In the Amazon, indigenous people often use brightly-colored frogs to poison darts for hunting and warfare. While America has few amphibians that I would call "dangerous," a predator can get nauseous from eating some species of frogs.
In this picture, the horse is likely curious. Like dogs, horses like to sniff things that are new to them. It's kind of a way of saying "hello."