The Player's Handbook has this to say about Controlling a Mount:
The initiative of a controlled mount changes to match yours when you mount it. (...) A controlled mount can move and act even on he turn that you mount it.
If someone is already controlling a mount before a combat starts, does the already controlled mount need to roll for Initiative ?
If so, then I suppose the result would instantly get overridden by the mounter's initiative.
If not, then it would bring an interesting scenario if, during the combat, the mounter dismounts the mount -- perhaps, at that point, the mount would need to roll initiative.