Per RAW: No.
So you are on your GMs mercy there.
a) well you could make a case for it's possible to change the mount to something else (se below)
b) "The creature must be one that you are capable of riding and is suitable as a mount" - That part is pretty clear.
Now Nature oracle says: "This mount functions as a druid’s animal companion, using your oracle level as your effective druid level" - so far so good.
And Druids say: " If a druid releases her companion from service, she may gain a new one by performing a ceremony requiring 24 uninterrupted hours of prayer in the environment where the new companion typically lives. "
So if the druid can get a new mount so can the Oracle.
So you could argue that the nature oracle MUST start with one of the listed mounts (wolf, pony, camel and horse) - but can choose another later. But still one he can ride...
And really the nature oracle get ONE great revalation, one of the druids awesome abilities, if he is stuck with a horse - just play a druid - or say you would rather play a nature oracle since it's LESS overpowered.
But the rules are a bit unclear about can you change the animal to something else or not - but I would allow it - just to avoid a druid...
The wording is identical to the paladin and cavalier, so I'd say the stated limitations apply.
I wouldn't mind allowing the nature oracle to get some other kind of animal companion. It wouldn't be overpowered anyway, and might fit the character better.
Although I don't think the druid has that much more than the nature oracle, if you don't want to play a wildshape-melee-fighter.
Combat Training does, in fact, make the horses hoof attacks primary attacks. It was discussed in an official FAQ.
It is a little awkward to find but it is listed under the entry for a Horse. They have this trait:
Docile:
Unless specifically trained for combat (see the Handle Animal skill), a horse's hooves are treated as secondary attacks.
Other than that, Combat Training is a suite of tricks that get grouped together making it easier to train them with just 1 check. So it gets the attack, come, defend, down, guard, and heel tricks
As for the stats of a horse... you just use the stats listed under the Druid Animal Companion feature in the CRB
at 9th level your horse has
Size Large;
Speed 50 ft.;
HP: 60 (8d8+24)
AC 23 (+3 dex +10 natural armor);
Fort: +9 Reflex: +9 Will: +3
Attacks: 1 bite +11(1d4+5), 3 hooves +11/+11/+6(1d6+5);
BAB: +6
Ability Scores Str 21, Dex 16, Con 17, Int 6, Wis 12, Cha 6;
Special Qualities low-light vision, scent, Combat Trained, Link, Devotion, Share Spells, Multiattack (which now gives an extra attack with a -5 if you don't have secondaries, which the horse does not)
It would also have 2 ability score increases to put wherever you like, 8 skills, 4 feats, it can learn up to 12 tricks above and beyond combat training (4 bonus from companion progression and 2 each for every Int point above 2)
I am curious as to why the bite is so much lower than the bites of other large creatures, especially since the horse doesn't have reach, but that is some question for another post :)
Well, I'll try to answer it here anyway :)
The horse bite attack was a d4 in 3.5 (don't know about previous), and PF seems to have stuck with that.IMO it seems reasonably, as the horse is typically a mount compared to the frontline fighting tiger - despite that the tiger can be mounted. And for what it is worth, while I don't want to be bitten by a horse, I'd choose it over the tiger bite any day.
On reaching from different squares, my guess is no. But I am not aware on official word on it. There was a recent thread regarding choosing squares of large creatures to attack.