In the 9th piece of DLC since the games' launch in May 2018, Riders of Hyboria, will finally bring horses and mounted combat to Conan Exiles. While the mounts are a free update, Riders of Hyboria will cost $10 (or included in the Year 2 Season Pass). More details will be incoming as the DLC, Mounts, and the rest will not be releasing until December, but will push to all platforms: PC, PS4, and Xbox One.
More details can be found on the official site: https://www.conanexiles.com/blog/