Many years ago a girl friend of mine had the idea of making a make-up bag that had some form of cooling gel within the bag material. The idea being that you placed the bag in the freezer overnight and during the day it would keep your make-up cool. Apparently lipstick was particularly prone to melting once above 25ºC. She never did get around to even trying to make a prototype – but I think such a design would sell especially in countries with a warmer climate than ours.
Turning to your idea, you can buy gel packs which are used for cool boxes that are made up of sheets of plastic with cells ‘bubbles’ of cooling gel trapped in a regular pattern. You could try making a pillow using such gel packs, but you would have to ensure that you had sufficient insulation within the pillow material to avoid frost bite – yet thin enough for the user to gain some effect.