You can not have a Warhorse as beast companion.
Beast Mastery: You gain a beast companion, chosen from one of these categories: bear, boar, cat, lizard, raptor, serpent, spider, wolf or horse. (Martial Power page 38 + Dragon 392)
A Horse Beast Companion is not a Warhorse in any way concering rules. Your DM could houserule a Warhorse is a horse, but I would advise against it. It would be overpowered, as a Warhorse is quite more powerful than any of the allowed types. (HP, trample, defenses, attack, damage)
The horse as a Beast Companion is weaker than a Warhorse for balance reasons. Changing HP and Defenses is not enough, change damage too, for trample as well.
Trample and Charger could be added at the cost of one feat each if they are usable at-will, or both for one feat if usable once per encounter. Still, trample should do 1d8 damage.
I would give you a free Saddle of Strength, it takes up the slot of the much better Impenetrable Barding anyway.
You need the Beast Rider feat for it just like with any other Beast Companion. For this reason and because of the better feat support, I would still go with a refluffed Bear.
Mark of Handling gives feat bonus to mounts, and feat bonus to beast companions. Feat bonuses do not stack, so no, it is not +4 speed +2 AC.
If your animal is tame, then you can ride it. In the Ride skill description, it says about riding animals:
When reared from birth, the following animals can easily be ridden by Small or Medium humanoids, depending on the riding animal's size.
This heavily implies to me that you can ride tame animals regardless of what tricks they know through Handle Animal. However, without knowing tricks, the animal will be very difficult to use practically. You will likely need to make ride checks to control your mount in combat if it hasn't been trained in combat, and you will need a DC 25 Handle Animal check to make it do anything that it hasn't been trained to do already.
You can mount a tame lion that knows Come and Stay, but it will be difficult to bring it into combat, and you won't be able to have it walk alongside you without a DC 25 Handle Animal check.
Best Answer
Sounds like a Plot Hook
Other answers have looked at the history, and pointed out that simple "re-training" isn't necessarily a realistic answer.
BUT
The DnD world is deliberately full of magic. It seems fairly likely that you aren't the first person to say: "I have a nag, but I need a warhorse!"
I could envision mages who specialize in this transformation, or items that can perform it.
Think about the level of risk / certainty you want, and take it to the DM.
Variations could include:
"I'd let an apprentice practice on my horse, and if it works, I get a free warhorse."
"We'll recover the item for the King, and just use it on our own mounts on the way home."
"I'll throw some money at the mage, and he'll transform my horse."
All are valid, and any could be fun under the right circumstances.
To be a little more concrete:
The difference between a warhorse and a draft horse is 350gp. Trivially, if you say "A wizard can transform your horse for 350gp." This is "balanced" and should not cause any problems at your table. It would be equivalent to selling the draft horse and buying a warhorse with 350 gp and the proceeds from the sale.
If you're intended solution is more complicated, the risk should be appropriate for 350gp.
In the case of an apprentice practicing the spell, you could select a risk of spell failure that fits the stakes. Having the spell accidentally transform the horse into a CR 10 enemy is probably not balanced - 350 gp is not a significant sum for a level 10 party - but a risk of getting fined by the local guild for enabling unsanctioned transformations, or the risk of costly material components being destroyed rather than returned, or even the risk of the horse just dying are probably appropriate risks.
Perhaps all those risks are present, such that on average the cost is around 350gp, but there's a chance it could be either free, or far more expensive.
And, as always, if the players find themselves in debt, they may have to pay the local guild with services rather than coin.