"Get off your high horse"
means to stop being so prideful and full of your self.
Nothing. The correct idiom is "get OFF your high horse," meaning stop acting so conceited as if you are above everyone else.
Getting on your high horse means that you are looking down on someone with a haughty or superior attitude.
That phrase means exactly what it says, so no, it's not an idiom.
important parts
Condescending or supercilious toward
High
This is not an idiom. Idioms make little or no sense unless you know the definition. This sentence makes perfect sense, so it is not an idiom. The dead fish smelled so bad that even as high as Heaven, you could smell them.
This isn't an idiom - it's talking about some animal with their tail held high, flying behind them.
Very, very small.
"Sky high" just means very high. You usually hear this as "blown sky high," which would mean either (literally) something exploded and was thrown high in the air, or (figuratively) that someone's plans were thoroughly destroyed.
The meaning is that it is the right time to do something.
It is not an idiom - it is a line from an old television cartoon called Rocky and Bullwinkle. Rocky was a flying squirrel. (Bullwinkle was a moose).