Which mission are you on exactly?

When you say "under military" are you clicking on the military icon and than clicking on the military workshops icon? The horse ranches should be under there.

I am on Zeus and Europa. I must get 50 people in a residence. Under military, trireme wharf and armory are available, but not horse farm.

If it's not there, then it is not yet available in this episode. It will possibly become available in later episodes of your adventure, but not during the one you are currently playing. You do not need horses to get people into residences (= lowest state of elite housing), only to upgrade them into estates (i.e. highest elite housing) which is not required for your mission. To achieve the "50 population in residences" milestone, try building a few more elite housings and make sure people move into them (i.e. enough culture etc.).

From the sounds of it I would say your elite housing is empty. Make sure the appeal in the area is high. Each housing unit should have access to 3 cultural venues. No idea what that means in that particular episode. Also, you need the basics of housing, food, fleece, and oil. Water surprisingly enough is not needed for elite housing.

Biggest thing though is to make sure that appeal is up. Use Avenues/Blvds, place some monuments if you must, parks, whatever. But you can have all the stuff required and if the appeal isnt high, they are not moving in. I dont even think you can place it without a minimum if I recall correctly.

Don’t recall how many a Residence holds either but I do recall its low. Will likely need 10 or so.