If frogs were taken out of the food chain, how would this affect snakes and owls?

All of these organisms—the frog, the snake, and the owl—are considered to be “heterotrophs,” meaning that they must obtain their energy from external sources (i.e., they cannot create their own). Furthermore, they are also “consumers,” which means that they eat other animals in order to acquire this external energy. However, in the simplified food chain that you have provided, none of these organisms are likely to be what biologists call the “primary consumers,” meaning those organisms who fall at the bottom-most energy level of consuming organisms. To understand how removing the frog from the food chain would affect the other two animals, let’s first consider an expanded, full version of this simple food chain.
Grass -> caterpillar -> frog -> snake -> owl
Here, grass is an autotroph (meaning it produces its own energy), and the caterpillar is the primary consumer, because it is the first level up from the non-consuming member of the food chain. Typically, biologists recognize the disturbances at lower levels of a food chain have more drastic consequences than those that occur further up. Therefore, if you were to remove the frog, the snake would lose its primary source of energy, leading to a reduction in its population. Consequently, the owl would similarly suffer because of a dwindling snake population, and one could reasonably expect a drop in owl numbers as well.
However, things are never so simple in nature. A decrease in the frog population would correspond to an increase in the caterpillar population. As such, it is likely that another organism in this hypothetical ecosystem would take the place of the frog once this new abundance of caterpillars began to invade its particular niche. This could be something like a lizard. Once the lizard population began to increase, the snake population would find a substitute energy source and similarly experience a rebound in numbers. This rebound would then correspond with a rebound in the number of owls.
Therefore, in the short term, removing the frog from the food chain would have a negative effect on the numbers of snakes and owls in the ecosystem. However, over the long-term, substitute sources of energy would neutralize this effect, leading to a stabilization of the overall population.