Glue was originally made from animal collagen which can be found in skin, bone, and tissue. In fact, glue has been made from animals for a very long time in history.
White school glue is not made from horses. In fact, while it originally included milk in the ingredients, the traditional school glue you are used to is now all synthetic.
You see, there is still a use for animal-based glues. These are used in different industries but most commonly the furniture industry. Aside from furniture, animal glues can be used for bookbinding, glass making, etc.
The types of glues that are made from animals utilize the collagen found in the horse. It can be extracted from hooves, skin and bones by boiling the body parts. You can even make glue from blood.
Most glues the average person encounters in their day to day life should be synthetic glues. This is especially true for glues common to primary schools. Is glue made from horses? It can be, but probably not very much anymore at all.