Word "конный" is used for things that are somehow related to horses and the uses of horses for man's needs: "конный двор" (stables), "конный завод" (stud farm), "конная тяга" (horse traction), "конный полк" (cavalry regiments), "конный разведчик" (mounted scout) etc.

Words "лошадиный" and "конский" are used for things that are connected directly with the horses themselves as physical beings: "лошадиный/конский череп" (horse skull), "лошадиное/конское ржание" (horse neighing), "лошадиный/конский помет" (horse dung), "лошадиная/конская доза" (dose for a horse — an idiom meaning "a large quantity"). These two adjectives have different genders, and the default one (in cases where the horse's actual gender is unimportant) seems to be "лошадиный".

I hope now you can see the difference in their usage better.

Word "конный" is used for things that are somehow related to horses and the uses of horses for man's needs: "конный двор" (stables), "конный завод" (stud farm), "конная тяга" (horse traction), "конный полк" (cavalry regiment), "конный разведчик" (mounted scout) etc.

Words "лошадиный" and "конский" are used for things that are connected directly with the horses themselves as physical beings: "лошадиный/конский череп" (horse skull), "лошадиное/конское ржание" (horse neighing), "лошадиный/конский помет" (horse dung), "лошадиная/конская доза" (dose for a horse — an idiom meaning "a large quantity"). These two adjectives indicate different genders of the horse, and the default one (in cases where the horse's actual gender is unimportant) seems to be "лошадиный".

I hope now you can see the difference in their usage better.