Apply colors to a mesh with a splatMap

I'm generating a mesh using a heightMap to which I add some PerlinNoise so it doesn't look all flat.

What I want to do now is color that mesh so that low grounds are green, medium brown and hight white (to make it look like a very simple mointain with snow at the top). To do so I created a splatMap from my heightMap hopping I could assign colors to areas I know will be around given height.

I wrote a shader to map the splatMap to my colors of choice, it looks like this :

 void surf (Input IN, inout SurfaceOutputStandard o) {
             fixed4 c = tex2D (_MainTex, IN.uv_MainTex);
             o.Albedo = c.r * _ColorPlain +
                        c.b * _ColorMountain +
                        (1-c.b-c.r) * _ColorTop;

             o.Metallic = _Metallic;
             o.Smoothness = _Glossiness;
             o.Alpha = c.a;
         }

But when I apply a material using this shader to my mesh it's just a mix of all three colors weighted by the areas on the splatMap. When I apply the material to a plane it looks just right (but it's obviously flat). I hope I can achieve the result I want, maybe not with a splatMap ? I don't know why it doesn't work when I try to apply the texture to my mesh.

Thx in advance to anyone reading this and I'll be happy to provide any other info that could help solving my issue :)