Personally, the idea that an animal companion isn't useful unless it is improving your combat attacks bothers me. You get this extra zone of control (including reaction attacks), they can soak attacks, they make perception checks (often better than the Ranger), and an optional attack without any changes.
Giving them an always on damage add or one attack advantage seems like a round of house ruling for the Fighter, Monk, and Barbarian will be in order. But at your table you can set the Ranger as best combat class if you want.
Fixing the Ranger by giving them both the beastmaster and the hunter (or Deep Stalker) plus then adding always on combat boosts from the pet seems like overcompensating (even with slightly lowering their high level spells while giving them scaling cantrips).
But I do understand a little Paladin envy.
But it would help to know - the Arcane Trickster gets an extra cantrip. Considering how much of the spell progressions power get's moved to cantrips it is relevant.
No objection, just pointing out it doesn't matter until 19th.
Warhorse is the best mount on the Find Steed list. Unfortunately it is CR 1/2 so not avallable within the normal limits. Giving it at 2nd plus Beastmaster bonuses would be very good. +8 for 13 (2d6+6) plus a potential extra attack for Trampling charge -- Save for Prone, then make a second +8 attack with advantage for another 13.
Draft Horse or Riding Horse are within the limit and lack the Trample. But then nothing is stopping anyone in the party from buying and using a Warhorse.
Do you have any specifics?