The idea is similar to an older build known as the Horse Oracle. Without getting too much into the nitty gritty of math, basically by 12th level your horse is considered a 19th level mount because of a variety of factors.
So what is neat about the Divine Hunter archetype? It helps make a stronger companion. Weirdly Divine Hunter does not mesh as well as you would think with Aasimar like how the Horse Oracle did.
For the race, it must be Human. Why Human? Because you want the Eye for Talent racial which will improve your companion. For the class go with Hunter and its archetype Divine Hunter, domain is always Animal. For the Animal Focus, always focus on things that buff the animal. A bonus to AC via dodge, stat enhancements, and the like. Mouse is a good aspect later on if your in PFS as you will stop at 12th but still have a way to give Horse the Improved Evasion feature.
Why a horse to begin with? Because, just like Horse Oracle, its hilarious to watch as the GM tries to figure out how to deal with a horse that is stronger than normal.
An excellent feat to pick up at 1st level is Huntmaster. You treat your effective character level as +1 higher than normal when determining the benefits of your companion/mount/etc. Also remember to get your horse some barding as it will need the extra AC. Also don't forget you may want to consider getting your horse some custom horseshoes like of the Cold Iron, Silver, or just +1 magic horseshoes.
Animal Focus choices:
Bat: Terrible. Remember your companion either has darkvision already or gets it from the template it gets at 3rd level for just being a Divine Hunter. The only saving grace is at level 15 for Blindsight... however for those in PFS you might as well ignore it as the cut off is usually level 12.
Bear/Bull/Tiger: +2 enhancement bonus to STR/DEX/or CON you say? Plus by level 8 it increases to +4? Sign me up.
Falcon/Frog/Monkey/Owl: Unless you got a really good reason to use these bonuses, they are at best situational and undesirable for the rest of the time.
Mouse: This is horrible for the early levels unless you really are in need of evasion. At level 12 however this becomes much more useful as at level 12 you get Improved Evasion, something your companion doesn't get till level 15 normally. It is also useful it you took an archetype for your horse that would normally get rid of its Evasion and Improved Evasion.
Snake: A +2/4/6 bonus to opportunity attacks and dodge bonus versus opportunity attacks. Fairly green to me, there is probably a build for it, I just don't see myself using it often unless I use the Bodyguard archetype.
Stag: Fairly yellow to me. Speed boosts are usually nice, however most quadruped companions come with a good movement speed anyway.
Wolf: Green. This could be handy if you wanted your horse to track like a bloodhound and it does have more uses than some others in this category.
You may also want to consider an archetype for your horse. My personal recommendations are Charger, Totem Guide, or Bodyguard. If you got Charger by the time you hit 5th, your horse will be immune to fatigue, by your 8th level your horse can run at full speed in heavy barding. Mouse might be an option as you lose evasion and improved evasion if you got your mind set on Hit & Run tactics. Also if you do go Mouse and manage to get yourself to 14th level so your Horse is at 15h, your Horse basically has evasion for Reflex, Will, and Fortitude saves.
If you go with Bodyguard it can yield for some interesting options with the Snake animal focus as your horse patrols around, and basically gets diehard for free while near you. While nearby, the horse gives you and itself the Altertness feat. At 15th level it gets an enhanced version of its diehard-esque ability. This also opens up the option for the Mouse animal focus as normally you lose Evasion and Improved Evasion.
Totem Guide is more of a support archetype. Your horse now becomes your guide as it can do spell-like divination spells if you got the spell slots for it. It can also get the Eldritch Claws feat for free which means you can save some money if you don't want to buy special horse shoes that are Cold Iron or Silver. As a full round action, targeting self or you, it can cast Guidance on its target. Also, it can never be raised as an undead, can deal full damage to incorporeal, its natural armor matters when regarding incorporeal touch attacks. Finally, it can talk to you and understand you. Like the other two, the animal focus Mouse is worth a look for replacing your lost Evasion and Improved Evasion.
There is the racer archetype, I wouldn't recommend it though as its more about moving fast, although at least it goes great with Stag animal focus I guess.
So by 5th level what do you got one might ask? Well a 5th level divine hunter and a 6th level horse companion. However the horse gets a few forms of benefits:
1) Eye for Talent, it increases any ability score the mount/companion has, of your choice, by +2 at character creation.
2) Domain, obtained at 3rd for being a Divine Hunter and fully comes together at 5th. As long as you picked the Animal domain you get a nice benefit. For your companion, you can increase any single ability score by +2 OR you can increase two ability scores by +1.
3) Otherworldly Companion, obtained at 3rd level for being a Divine Hunter. If you are good you get celestial, if your evil you get fiendish, if you are neutral pick one. For the sake of PFS lets assume you are a Neutral Good character, your horse gets the following for getting the celestial template: 5/evil (DR), Cold/Acid/Electricity 10 (Resistance), Dark Vision 60 Feet, CR + 5 (Spell Resistance), 1/day Smite Evil as swift action. To top it off, consider that your horse just got all of these benefits when you hit level four because of the huntmaster feat.
4) If you have been a smart shopper you probably at least got your horse some horseshoes made of at least Cold Iron or Silver as you can't just rely on that 1/day smite that horse has got. You also at least picked up some decent barding for the horse so it can last longer in battle.
5) Depending on your archetype you picked you get one of the following. Horse can talk to you (Totem Guide). Horse is immune to fatigue (Charger). Weirdly there is no 6th level benefit for Bodyguard, only 3rd/9th/15th.