Sorry, I overlooked your second post. Yes, ice can cause funny returns, but you should see false targets at altitude, too, in that case. Have you ever put your hands on the radome after landing, to check temperatures? An IR thermometer would be a neat device to have for this.
What does Maintenance say or do? Is the R/T in the radome behind the antenna, vs. in the pressurized E/E bay? It could be reacting to condensation forming on its parts, from being very cold, descending into warm, moist air. It should be immune to that.
GB