Cold shower when you have a high fever. Good or bad?

might be necessary if it's like emergency levels of fever, but your body heats up to help kill the pathogens and it's generally wise to facilitate that effort.

Can't say. When your body is trying to raise the temperature to cook an intruding virus or bacteria out, it will work back to try to keep it out again .-.
So maybe you did not help if the virus needs to remain at warmer temperatures to die off

It's how they recommend to lower the temp quickly, but unless you're at 109º, it really sucks.

....it feels like you are burning...from ice..
Very unpleasant experience I must say

It's fine as long as you are not feeling dizzy and are steady on your feet.

Good it brings your temperature down

Not cold. Luke warm.

Bad