You're talking about shooting someone with an instant cold pack. [WebMD](http://www.webmd.com/first-aid/tc/using-ice-and-cold-packs-topic-overview) recommends  keeping a cloth between the ice pack and the skin and limiting exposure to 15-20 minutes. It's not going to be very effective. 

I'm not sure why you'd want to in the first place. Even if you shot someone with a vial of liquid nitrogen you'd be looking at some added [frostbite](https://en.wikipedia.org/wiki/Frostbite). This will be unpleasant to whomever has been shot. But the arrow sticking out of them is of much greater concern.