I want to ask the woman in the row across from me to shut the airplane window
Why do you want the window down?
Because the window is too cold.
They paid for a window seat and they deserve to open or close it. You could buy the row out next time or ask for a blanket.
You don't get it unless you try.
I get it, they have every right to use the window how they see fit. There are controls above your head where you can turn the a/c of too.