Alright so when using a mount we have two options: command it or let it act independently (PHB pg. 198). Letting it act independently is the only way to get it to attack, given that it chooses to attack (which I would expect it to do if it's naturally aggressive or trained for combat). So if you have a warrior of a mount under you, he will be attacking separately from you, essentially giving you extra attacks.
When playing the Beast Master Ranger and using its animal companion however, we can only command it (PHB pg. 93). Letting it act independently is absent from the RAW and as such, it is not possible to have it attack without wasting your own attack on it. So, essentially, you're not gaining much other than versatility and range. You are not getting any extra attacks.
So, in my desperate efforts to care about the beastmaster class, I hatched the following plan. Play a small race. Make a medium creature your companion. Mount it. Let it act as an independent mount. Independent mount does whatever it wants, hopefully it wants to attack.
This would mean giving up on Bestial Fury (which lets the companion attack twice but only if you specifically issue the attack command), but that doesn't matter.
My question is can you let your companion mount act independently or do you have to use the Beast Master's commands to control him?
Best Answer
The Ranger's companion is ...
It is not trained as a mount. And ...
The rules are quite specific here; you do not need to use your action to command your companion to Cast a Spell, Hide, Ready, Search or Use an Object. Now some of these are not very useful but Ready has definite possibilities - "Ready to attack the first creature that attacks me" for example.
Moving on to what a mount can do.
If your companion is intelligent (unlikely) it will always act independently. If it has not been trained to take a rider (likely) it will always act independently. If it acts independently it is subject to the rules of the companion. If you command it, it will cost you your action is on the companion list of actions. If you don't command it, it acts as the DM sees fit.
If it is both unintelligent and trained to take a rider (like a horse) it must follow the rules for both a mount and a companion. If it is controlled, it can Dash, Disengage and Dodge at the cost of your action
The three options that any other mount gets for free (Dash, Disengage and Dodge) cost your action. So a companion horse is worse than a regular horse. Now, feel free to stop and call "stupid" but that would be a house rule.