the pump provides 2 things, one, it stirs up the water to oxengenate it. and second helps you filter it.
the water color is due to leaves and stuff settling and decaying in the water. i'm more concerned about the fish at the top. usually fish will head to the middle of a pond when it gets cold as that is where the water is most consistantly a good temp for them. can you run the pump even when it is cold? to give the fish air?