For champions/sovereigns, you need to go to a store and buy a horse/warg, then equip it in their inventory. They'll be available in the stores of any faction that has the right technologies researched (including yours, since you can design warg-riding troops.)
AFAIK, there's no way to upgrade existing footsoldier units to cavalry. It has to be included in their unit design.
Thank you!. Buying a warg in the store did the trick for me.
What I don't understand is why I can't use my own harvested wargs to upgrade my Sovereign/Champions. Wargs are very expensive to buy in the store. Selling them to other factions isn't very profitable, so the trick of buying them in the store and selling those in your stock to recover your money isn't worth it.
By the way, I'm playing vanilla FE (without the Legendary Heroes expansion).
