Don't be silly, turning the heater dial to cold doesn't stop the coolant running through the matrix, it just closes a baffle and redirects the heat outside and lets fresh air in. Chances are you will have a fishy smell (coolant), the smell subsides when the controls are at cold because its not being blown into the cabin.
You can leave radweld in the system, it protects the pipes and inhibits rust but I would remove it when not needed.
In the winter - you get cold, or have an electric heater. I hid mine next to the fan so the heat comes out the proper holes.