Insulate my windows from the outside?
I always strongly recommend the 3M plastic insulation kits. One of their main products is transparent tape and that is what fails with other brands.
Insulating too much might mean you are risking condensation between layers or similar. In the winter the air is dry enough for this to be unlikely.  I have never seen it. The kits come in Inside and Outside varieties but the inside is the easiest to use.
During a snow storm in Chicago that came to be known as Snow-pocolypse my 3M plastic held up. The wind was so strong against my balcony that the plastic was distended from the window over 1 foot. I stacked boxes against it to take the strain off. I've had similar storms since but the 3M has never failed.
On windows without plastic I can feel the cold, not the wind, move right through.