functions as a controlled mount while you ride it.
The restrictions on a Controlled Mount’s actions are explicitly limited to the rider’s turn:
The Initiative of a controlled mount changes to match yours when you mount it. It moves on your turn as you direct it, and it has only three action options during that turn: Dash, Disengage, and Dodge. A controlled mount can move and act even on the turn that you mount it.
[emphasis mine]
However, there are no such restrictions on a mount’s other action economy. For example, a Controlled Mount can still use its Bonus Action or make an Opportunity Attack using its Reaction.
RAW, is it possible to coordinate with a creature such that it Readies an action (e.g. an Attack, triggered by coming within range of a hostile creature) before becoming a Controlled Mount, and then later resolves that readied action as a reaction after it becomes a controlled mount?