On this page of The Witcher 3 Wild Hunt guide you can find walkthroughs for all side quests taking place or involving Oxenfurt. The solution explains, among others, how to act regarding the Rock Ogre and how to defeat him (optional) and how to track down and safely return the missing horse.
You will learn about this quest by taking a note from the notice board in Oxenfurt (M8,2). The note will inform you about strange noises coming from an island West from the city. Go to the eastern shore of that island (M8,3).
You will learn that a Rock Ogre singing redanian army's songs is responsible for the songs. He will be friendly, so you can talk to him.
During the conversation you can choose between two variants:
Option A - Attacking the Rock Ogre
You can attack the ogre. He has 13 experience level but he is not a requiring opponent. Use magic shield sign Quen and avoid his ranged attacks. Jump towards him from time to time, deal few hits and jump away. After few such rounds the Ogre will die. You can take some precious alchemy ingredients from his body.
Option B - Bringing the Paint
Continue the talk to the Ogre. He will ask you to bring him some paint. You will find it at one of the merchants in Oxenfurt. After you deliver it to him, you will receive another task - to paint a redanian eagle. You can help the ogre with that, the result won't be astonishing but the ogre will be happy. You can also convince him to paint the eagle by himself. In that case the result will be much better. No matter how you acted, the reward will be the same. You will receive some gold, few diagrams and many various leathers.
To receive this quest you must talk to a Peasant standing next to a small house east from Oxenfurt (M8,7). He will want you to find his horse which has probably run away.
To track it down use witcher senses. Walk through a dirt-track for a while, then turn left towards the small lake. You will lose the track at the lake but you should easily find it back on the other side. Follow it until you reach a group of Scoia'tael on level 10. Defeat them. Your questgiver's horse is gray. For taking it back to the Peasant you will receive 20 crowns. It's important to lead the horse directly to the special place for him, only after that the quest will be accomplished. You can pick another horse as well, for leading him to the questgiver you will receive 50 crowns.