I would not suggest the ice in the back pocket at all. It may sound ridiculous but, frostbite is a serious concern with all that ice in close contact with the skin on your back. It would be fine to place some on your neck for a minute or two, or even if you did a small amount and moved it from pocket to pocket as long as you avoid prolonged contact to any one area of skin.

We learned this the hard way while riding ragbrai this summer when my riding partner decided to take a siesta after lunch with an icepack around his neck. Everyone else on the ride had sunburned necks, but my friend had frostbitten neck.