Based on the given information about the food web and the roles of different consumers, the animal most likely to be a keystone species would be the deer.
Keystone species are those that have a disproportionately large effect on their environment relative to their abundance. Deer, being herbivores, help maintain the vegetation levels which in turn supports the entire food web. If deer populations are drastically reduced, it could lead to an overgrowth of plants that may alter the habitat, affecting all other species in the ecosystem.
In contrast, the other options like frogs, grasshoppers, and mice, while important, typically do not have the same broad impact on the ecosystem as herbivores like deer.