Like a real horse, you may need more bones in the neck. Study the anatomy of the animal you are modelling, particularly the skeleton and build your armature the same, or you cannot expect your model to behave like the real thing. You can use bendy bones for the neck, and the advantage here is you can always increase or decrease the number of segments to get the right performance. Also you may need to constrain some of the neck and spine bones, so they do not bend unnaturally relative to each other.
I cannot see any connection between your spine, which should also be multiple bones, and the neck or shoulders, this lack of bones will mean a poor mesh weighting and unrealistic distortion of the mesh when you pose the model. You need to put a lot more time into getting your armature more like a horse skeleton, or the model will not work like the real thing.
You did not post any blend file, so I cannot comment on the distribution and density of vertices in your mesh, this will also effect the realism of your model. Insufficient polygons equals poor distortion when posed, as does too many polygons. Do you have any three sided polygons (tris)? Do you have any polygons with more than 4 sides (ngons)? If so you will need to get rid of these so the model is all quads (4 sided polygons) before you try the parent the mesh to the armature, then you will almost certainly need to tweak the weights to get the model to pose correctly.