I got too invested in those stupid horses, so a long post incoming. If no one sees it am gonna cry.
So starting from the common one. This variant is your usual RadHorse, but it doesn't keep close to settlements, so chances of seeing it are rather low. It lives in herds and doesn't like people. Rather strong because of its six legs, but its speed is nerfed - the legs have a small range of movement and the horse has the tendency to get tangled up in them. They're simply too big to move too fast, or too fluidly. Thanks to it's two heads the oxygen filtration is peak - one head inhales, other exhales, so they literally can't run out of breath. However, it's not recommended to try and approach them - they'll kill you. Live in mildly irradiated zones.
The rare ones keep closer to humans so it's much more likely to spot them, or catch them. They can't be ridden, however, because their four legs are too little to support the additional weight of the extra head + the rider. They can run really fast - four legs means wider range of motion, but only on short distances - not because they run out of breath, but because their legs give out. If push comes to shove they simply go zoom and when they're safe sit down like dogs. They're rather friendly and don't attack or run away if approached. Live in lowly irradiated zones.
The bred variant happens when a pregnant rare mare is caught and fed radioactive paste, so the foal is born with an additional pair of legs. They get the temper from the rare variant with the physical stats from the common one, creating a perfect working animal. Their agility is better because they're trained on obstacle courses to have better awareness of their bodies. Would approach of their own volition, since they're human raised. Come in weird colours and sometimes with weird body mutations.
This is your average horse lol. They have higher stats because of being irradiated and they tend to be smaller than the other variants so their agility is maxed. They live in zones where radiation is really low so there's not many of them. Wouldn't run away, but wouldn't approach either.
Now this one is a no no. They would chase you on sight and kill you, no running away from this one. Thankfully they's very little of them since they're simply the epic variant, which at some point been exposed to absurd levels of radiation and mutated (some of them lived near Shady Sands and when the bombs fell, welp--). They're very old, chances are that some of them were regular horses and remember the times before the bombs. Either way, they don't come in contact with humans, since the radiation in their zones would be deadly to anything considered alive. They can come in weird colours because of irradiation levels.
Now this is for the bred one and how it would be ridden. The reins criss-cross like in carriages led by more than one horse. But, while I do ride horses, I've never drove a carriage so idk how it works.
Anyway, huge thanks to @demonswalktheearth for pointing out to me that the majority of hooved animals in fallout actually have two heads. But since there's no horses in the games (which I've never played, so I didn't know abt it either) I decided to pull my own headcanons outta my ass. So now I have ✨options✨.
They live longer that regular horses - their age can be counted by the number of eyes on their bodies, bodily mutations (fe glowing spots) and the yellowing on their teeth.
Also, there's no usual breeds anymore. They simply look like a combination of breeds which lived in the area when the bombs fell. Some common traits is overal baldness exept few tail hairs, thicker skin, two hearts and being omnivorous.