I've mended Breyer SM legs with superglue gel before, it sticks permanently and quickly, and stays strong enough forever afterwards.
It doesn't
have to be the gel one, if that's just not available there - the liquid also works, but it's much harder to control as it's so fluid it will just go everywhere before you've even realised it's got out of control, and then you've got weirdly hot-feeling fingers glued together, or one speck on your finger printed elsewhere on the model and you've got a spoilt paintjob. The gel one stays exactly where you put it
It also has the advantage of drying with a bit more bulk to it than the liquid one, so it acts as filler to smooth out the join and fill in any voids left by the plastic having bent as it broke.
A lot of people say you
have to drill and pin broken legs on models, but for a small light horse like a Stablemate, with a sedate life on the shelf and gentle occasional handling for dusting or re-organising etc, superglue is enough - pinning might be more trustworthy if you have a large heavy one in an action pose where one leg takes much of the weight, or want to keep wrapping and boxing the model to take to live shows, but not needed for a simple standing-four-square SM.
I was relieved as I scrolled down and saw her leg was
black at the point of breaking, as this makes the fix ten times easier for you!
Here's how I'd do it...
Test the ends of the leg together without glue first, get really sure in the exact angle you need to be aligning them at. Don't fret too much if it's not a clean break, any rough edge can be dealt with later.
Apply a dot of glue to the end of the leg still attached to the horse. If your glue doesn't have a very fine nozzle (I don't know what brands or packaging types are available there), apply it to a pin first, then use the pin to dab it in place.
Leave it a few seconds while holding the model upside down - the glue won't set instantly and I find it's better to let it half-dry beforehand rather than while trying to hold the leg perfectly still all that time.
Press the leg into the glue, checking your alignment from the front as well as the side. Again, the glue isn't instantaneous, you have time to check and double check before it'll grab too firmly to re-adjust.
Very quickly wipe away any excess glue which has spilled to the side, as long as you move your finger fast you won't get stuck to the model, and the glue will peel off skin really easily later on, you don't need solvent or anything, just a bit of water to loosen the edge and it all lifts off, pain-free.
Hold the model carefully for about 30 seconds, just to supervise and make sure it stays in one piece while the glue finishes setting. You shouldn't have to touch the leg to keep it straight, but occasionally it does need a slight support or nudge in the first few seconds to stop it moving while the glue's still soft.
Once the glue is entirely solid, you can inspect the smoothness of the join. And here's where you're really, really glad the model is black - it's the easiest colour to match, and you don't have to worry about translucency of plastic or speckling or shading, it's just plain black and any paint or even ink will match it.
If the mend is neat but you can see a tiny tiny bit of the white plastic showing like a hairline crack, just rub a little paint or even black ink in there, and it'll be hidden enough for shelf display.
If you had slightly too much glue, or the plastic was a little bit warped out of shape leaving an overlap, and the join is lumpy
outwards, you can use some fine sandpaper or one of those fine cardboard nail files to rub it down. Don't worry about marking the paint a little bit on either side of the mend, that will paint over just fine.
If there's a groove or dent in the leg, you can apply a bit more glue in layers and leave it to dry, then file it down as above. I really wouldn't bother investing in sculpting material just for such a miniscule amount of filling a snapped leg would need - even though I have the stuff in stock at all times, for mending try I to avoid using it just for speed and simplicity sake - the glue itself will fill that space.
Finally, apply your paint - expect to use three or four thin layers in a smudging motion, leaving drying time between, rather than trying to cover in one layer brushstroked on. I know you're familiar with painting of all kinds, and have currently got paints in the house cos I remember seeing your custom even though I can't remember his name, so I won't go through what to buy, you're good for that section of the process
Most brands of acrylic paints have a slight sheen to them which I find matches really well with the finish of Breyer's OF paint.
But if it's looking slightly more matte than your model once it's dried, a careful polish with a bit of fleece or blanket puts just enough shine on it to blend in.
And if it seems to be more shiny than the OF bits of the leg, give it one more rub with a dry soft paintbrush while it's drying, and that mattes it down a bit!
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Thankfully only one of them broke, but I am pretty bummed about her! I have used acetone in the past to fix snapped legs, and it works pretty well as long as the horse doesn't move much again, but it's also far from secure. I had a unicorn horn re-break multiple times with acetone. And this one isn't a very clean break, it will continue to look broken even if I got it stuck back on. What are my options? Does anyone have any beginner level processes for patching a break? I don't currently have any kind of sculpting material or the correct kind of paint - what would I get? I can tell it wouldn't need a ton of either, I just don't know what I'm looking for or how to use it or if it will work well (or if it is expensive?). I don't really mind if she's repaired and not "mint" since I don't plan to sell her, but I would like her to stand and look whole on the shelf again! She is one of my childhood horses that made it this far, only to be struck down at the least likely time. 
