The description of find a steed He says:
Summons a spirit that assumes the form of an unusually intelligent, strong and loyal steed, creating a lasting bond with him. […] Also, if your steed has an Intelligence of 5 or less, your Intelligence becomes 6, and you gain the ability to understand a language of your choice that you speak. […] While your steed is less than 1 mile away from you, you can communicate with it telepathically.
Search Steed invokes a mount that is under the paladin's control, regardless of the intelligence of the mount.
And another relevant exchange:
Twitter user: "excellent, and will you follow the commands as best you can?"
Then, in practice, the player would have control of the steed's actions, at least when the pitcher is one mile away and is able to command the steed. The spell does not specify what happens if the caster dies or is unconscious, so the DM will probably take control of him in that case; similarly, if the steed is more than 1 mile away and, therefore, can not be sent directly, it would be reasonable for the DM to control it as long as it continues to comply with the most recent orders of the launcher.