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Cold water is to stop the cooking process in the meat. Not saying you should not do this.
Lets say your IT of the meat is at 152* Yes cold dunk them just for a min to stop the heat. Now if you check the meat IT and its at 149-150 You can pull from the smoker, skip the cold water and hang or rack the sausage at room temp and they will IT by themselves.
I put the sausage in brown paper bags and in the fridge a couple days before cutting and vac sealing but this is your call. They are ready to eat right out of the smoker if you wish.
Target IT of the meat your looking for is 151-152* Anything higher your risking a fat-out of the meat and it will be greasy.