The find steed spell allows you to summon an intelligent mount. Everyone is trying to use their character's readied action to attack; why not flip the script?
A trained steed or a Intelligent steed, acting on its own turn, can ready an action. Ready Actions use up your action, but you still get movement.
The steed can move you into range, and ready its action triggered to dash away after your turn. (Ready action is either a single action or movement.) Utilizing a reach weapon (I.E. Lance, bardiche, etc.), the horse can effectively do "drive-by attacks", pushing you into range, allowing your attacks / bonus attacks / action surges - and at the end of your turn it moves away.
If the horse is trained, it can be trained to keep a 5-foot gap between it and the enemy, then continue in a straight line beyond the target after its rider completes its attack (Jousting). Or it takes the defensive action in the event of a melee brawl. If it is an intelligent mount, the mount can choose the best course of action.
Cavalry mounts were trained to be steered and controlled using nothing more than spurs and weight shifts of the knight utilizing them. Which means the mount does not have to necessarily understand a language to receive commands about what it is supposed to do on it's turn. Whether or not it follows those commands depends on the handler and the conditioning of the horse. So, assuming the rider chooses to go 2nd, he can use his knees and spurs to give commands to the horse about what it supposed to do on it's next turn (which, if you want to force some kind of action, the knight has to use his movement to appropriately wiggle his knees and spurs against his horse to relay said info).
Onto which goes first...
The initiative of a controlled mount changes to match yours when you mount it.
This means that on your turn you "Control" and "Release" the mount to reset its initiative. And then you let your mount act first (yielding initiative to your mount since your initiatives take place at the same time).
If a tie occurs, the DM decides the order among tied DM-controlled creatures, and the players decide the order among their tied characters. The DM can decide the order if the tie is between a monster and a player character. Optionally, the DM can have the tied characters and monsters each roll a d20 to determine the order, highest roll going first.
So it's up to the DM to determine if it will be the mount, or you, using their reaction. Is the mount considered a player-tiered character or monster...
Just food for thought. Basically it comes down to the rider micromanaging the mount or giving general instructions for the mount to act on it's own accord. A Draft horse would likely run away or get spooked if it got too close to hostile creatures if left to it's own devices, which is a reason for there to be a distinction between a draft horse and a war horse.
So long as an intelligent mount has been trained, initiatives can be matched.
Alternatively, you can have your druid Wild Shape to be your mount... whistles innocently
Resetting the initiative on intelligent mounts:
RAW says, under Controlling a Mount (from PHB, pg. 198):
You can control a mount only if it has been trained to accept a rider.
Which means that if you are using an intelligent mount that HAS NOT been specifically trained to act as a mount, it will act on it's own initiative. But if you and the intelligent mount train together, you can achieve "Mount Control", thus allowing you to reset the initiative. Find steed has this built in - but using something like a Dragon, does not (unless you and the DM work it in).