The origin is unclear, but it most likely refers to a confusion between horses of a similar color. The idiom means that the new subject is totally different.
It is red tape.
Whenever you see an idiom stating that something is "a different _______" (a different kettle of fish, a horse of a different color, etc), it just means that whatever topic has just been mentioned is totally different from what was spoken before. For example, if the topic of conversation is gambling, and someone mentions the game of bingo, a person might say "That's a whole different kettle of fish -- bingo isn't really gambling at all."
Nothing. The correct idiom is "get OFF your high horse," meaning stop acting so conceited as if you are above everyone else.
One such idiom is "Don't look a gift horse in the mouth."
idiom
Getting on your high horse means that you are looking down on someone with a haughty or superior attitude.
A cliche
As in "I am so hungry, I could eat a horse"- means you are extremely hungry- since a horse is VERY big.
The color of the herring in the idiom "-herring" is red.
idiom
From horse racing, where they judge the winner of the race by which horse's nose crosses the line first.
An idiom is an expression, the meaning of which is dependent on cultural context and social understanding. The meaning of the idiom is not predictable based on its constituent elements, but is merely an expression. An example of an idiom is "kicked the bucket". These words are not taken as literal, but as an idiomatic expression.