Check the ignition switch and/or relay. If the relay is intermittent, the current will only be passed when it's cool.
Check/replace your fuel filter. Many times cold weather has a tendency to solidify contaminants in fuel, which cause a partial clog on cold start. Warm fuel suspends the contaminants better, so the filter can clean the fuel as it passes easier.
If it's the IAC, you should be able to disconnect it and unbolt it from the TB. Get some carb or TB cleaner and spray the spring in the IAC to remove the carbon build up. It's a good idea to clean out the throttle body too, but just spray a rag with the carb or TB cleaner and wipe it clean. Do NOT spray it directly into the TB. Although it is "ok" to do so, you have to do that with the engine running to prevent the liquid from settling and entering the combustion chamber in full liquid (not atomized/gaseous form). You run the risk of stalling or, at worst, hydrolocking the engine.
More than likely it's the water that you're using. It's recommended to use Distilled water as the calcium and magnesium have been removed. Tap water has those minerals, which cause scale/buildup and lead to rust.