To do a painting on a window you need water-based paint with a few drops of dish soap into each colour or tempera paint. If it is easier to draw out your plan, there are also markers for windows which is what I used when I did the Grinch. However, I did the Grinch on a tinted window and it was hardly noticeable from the outside, especially from a distance.
I did the snowman on a clear window. It turned out excellent, inside and outside view.
*When it is time to remove the painting, just use soap and water or window cleaner.
Creating other colours using primary colours
Blue and Red = Purple
Blue and Green = Aqua
Blue and Purple = Violet
Black and Red = Burgundy
Red and Green = Brown (add black or white to darken or lighten)