I would be guided by how it will look when the foam is on, you can carve foam quite effectively so could shape it into the muscle shapes easily enough and use a glue gun. From what I can gather from puppet makers there is no other way to attach foam properly.  spray adhesives just don't work.

I would ask why you think you need foam.  Is it because you want to create a softer touch?   Or is it padding for children to sit on?
If the latter, you probably need to think in terms of upholstery.  Certainly, as Charlotte says, putting the foam where you need it, but perhaps going further and creating fabric covered shaped pads that you can tie or fix with velcro.
If neither, you could just apply fabric using PVA.
DavidO

Most spray adhesives will 'eat' foam, as will most spray paints. The carriers (usually petroleum based) are corrosive to the foam and will literally eat holes in it as you watch.

There is a white glue that is made specifically for foam, but it takes at least 12 hours to dry. It comes in those fat tubes like caulking, and you use it in a caulking gun. Hardware stores carry it, because it is used with the sheets of foam wall insulation.

Regular white craft glue (PVA) works all right, except for the drying time, and it is often best to clamp or weight the pieces for the best adhesion.

Hot glue works best, as long as you aren't applying a line of it that will show under a thin fabric (etc). If you have a choice between low-melt and hot-melt glue sticks, use the low-melt. The very big advantage that hot glue has for building such things as this is its speed. Nothing else can touch it.

For your horse, I would use the glue gun for applying the foam to the PM, but I would use the white craft glue for applying your fabric to the foam or the PM.

Sue