I would make up a good papier mache pulp mix and work it well down into the gap, leaving it slightly mounded above the opening.  Let it dry very thoroughly, then sand it down with a fine sandpaper to the level of the original material.  Use a sanding block, not just your fingers.

There's no indication which country you're in, but in the U.S. there is a yellow wood glue referred to as YELLOW CARPENTER'S GLUE, and one reliable brand is "DAP Weldwood Carpenter's Glue", and another is "Titebond Original".  It is an Aliphatic Resin type of glue, if that helps you find it elsewhere.  It is common, inexpensive, and usually available practically everywhere that hardware and wood glues are found.  It is related to PVA glue, but don't let anyone tell you that it is the same -- it's not.

I am advising use of this particular glue because it works well with paper when diluted half/half with plain water, and it dries hard, which makes it possible to sand.  It is faster-drying than PVA glue, so don't walk off for very long if you've stopped at a point where drying would cause a problem.

Buy a smaller container of it, because it only stores well for a year or so.  For the same reason, I would buy it at a place that has a lot of turnover in products.  Old glue of this type is difficult to work with, clumps, and just isn't worth the frustration, so don't buy a gallon of it for longtime future use.

PVA (polyvinyl acetate) glue is the common white craft glue, and I would avoid that kind.  It is plastic-based, will flex even when completely dry, and doesn't sand smoothly enough for your purposes.  You need a glue that dries hard.

You absolutely would NOT want to use any type of epoxy glue, polyurethane glue, or hot-melt glues, or any of the natural flour glues -- they are not appropriate for this kind of work.

Take your time and do it right the first time, because trying to fix a mistake embedded in that slot would be a real problem.  Pay attention to the consistency of your pulp/glue mix:  it should be moist enough to stick to the inside walls of the crack, but not so wet that it's too wet.  The more moisture that is in your mix, the more the mix will shrink as it dries, and excess shrinkage can cause the mix to pull away from one of the walls.  Enough, not too much.

Force the pulp/glue mix into the crack for an inch or two (2.5 to 5 cm), more if you feel that would be better.  A flat piece of metal, like a piece of broken hacksaw blade might work well.

Build up the pulp a bit so you have an actual ridge of pulp (maybe 1/8" or 3mm) extending out of that crack.  If you smooth the pulp to the level of the existing papier mache, it will shrink a bit as it dries, and will probably leave a shallow trough, which is more difficult (but not impossible) to fill.

BE SURE to let it dry thoroughly -- I can't emphasize that enough.  It dries faster than PVA, but you don't want any moisture left inside.

When dry, check the ridge:  has any part of it shrunk below the surface of the original level so it needs to be filled?  If so, mix up a bit more pulp and glue, and fill in the gap, again mounding it up so you will excess to sand down to level.

When dry, wrap some sandpaper around a small block of wood, and gently work down the ridge.  You may want to take off most of the excess with a medium-grit sandpaper, then change to a fine grit as you approach the level you want.

Repeat the filling of gaps if you find any you missed, let dry and sand again.

For the peeling paint, I would peel off any of it that is already lifted off the surface, and then use fine grit sandpaper to smooth the existing attached paint to you don't have an abrupt edge to deal with.

For finishing, maybe David can help you out better than I could. 

But keep in mind that repairs to antiques usually diminishes their value, no matter how well done.  If this is simply a piece that you like and would like to restore to its former glory for your own admiration, go ahead.

Sue

"Could you elucidate the why of "you absolutely would NOT want to use any type of epoxy glue, polyurethane glue" - it might be edifying."

Hey, who has more opinions than me?  But I did write that comment with this particular project in mind.

Epoxy:  it sets up fast and and dries in 15 minutes.  That's too fast for what the OP will be doing with this horse.  Also, it's toxic and needs to be used in a well-ventilated place, and handled with gloves.

Polyurethane glue:  "Gorilla Glue" is one of these, and they expand while curing, so you wouldn't want to use them inside any joint due to possible distortion or displacement.  They cure (and harden) very quickly upon contact with moisture (as in the air), and will start curing as soon as the glue leaves the bottle (and sometimes before), again too fast for this project.  They're also toxic and difficult to remove from your skin. 

Hot-melt glues:  Quick and easy, cheap and fast-setting, but the bond is not very strong.  If you even use it for attaching things to a PM box, the decorations will start falling off at some point in time.

Natural flour glues:  Wheat, rice or potato flour mixed with water, cooked or not.  I usually use these kinds for projects expected to have a short life, like pinatas or expendable toys for children.  Like it or not, organic glues like these tend to attract insects, rodents and some dogs (cats, not so much).  Spending time and money on an important project is discouraging when you find it perforated with tiny holes, chewed areas, or torn apart by a peckish Siberian Husky.  I've made some smaller, solid pulp decorations that were a little heavy on the glue, and they seemed to absorb moisture from the air even though they were sealed (maybe not well enough?).  And historically, I've never seen nor heard of any flour-based PM in the antiques shops.  I just don't consider them as having a long life.

Methyl cellulose adhesive does come from an organic source (usually wood), but is has been so highly processed that living creatures don't show interest in it.

Sue

Patraw, true on the seam, but I am totally ignorant about antiques.

I thought of clamping, but even though the crack is the full length of the horse, there's no way to tell what is still holding it together: bolts, a block, dowels?  Forcing it closed when there might be something inside holding it apart could cause more damage.  And the gap would still have to be filled- maybe better to use the depth of the gap for better 'tooth'.

Sue