Window Tint bogus ticket?

I am looking for legal advice pertaining to a ticket i recieved half an hour ago

The story is as follows...

It is winter around 2:27 AM and i was driving home with my windows down (weird i know but i like cold weather) when i pass by an officer. He pulls out behind me and pulls me over...

Now granted all my lights we're working, i am sober, and was not speeding or swerving or weaving.

He walks up to my windows (which are still down) and asks if i've been drinking, i reply that i had a beer two hours ago for my friends 21st birthday. He asks if i have any alcohol or drugs in the car and i reply no. and finely asks why my windows are down. I reply because i enjoy cold weather. he then tells me to roll my windows up and see's they are tinted and states "Tinted eh?" (Note my car was off, and parked with the keys out at this time)

He then proceeds to write me a ticket for window tint, when he never even had a reason to pull me over or reason to know they are tinted in the first place.

My question is should i fight this on the basis that he had no reason to pull me over, and my windows weren't up at all this night until he told me to put them up? Try to maybe get it dropped on the basis that i did nothing wrong and had no reason to be pulled over except that i was profiled as a drunk driver because i was out at 2:27AM with my windows down?

Also question two, if my car is off and parked with the keys out when he told me to put my windows up then i'm technically not operating the vehicle when he told me to put the windows up because there is not key in the ignition?

any input will be valuable, i have to show up in court no matter what.
Thank you in advance