[mannerheim]

There are several 'mathematical' ways you could phrase it (glossing over how to define the colour of a horse):

1) In a set of horses with size n, if horses A and B being both members of this set implies horse A has the same colour as horse B, then all horses in the set have the same colour.

2) In a set of horses with size n, and let f be a function on this set that produces each horse's colour. Then all horses in this set have the same colour if and only if the codomain of f on this set has size 1.

You could probably prove these are equivalent definitions.