No, that is not the reason.
yes it is:
Standard Weight Tank
The original ET is informally known as the Standard Weight Tank (SWT) and is fabricated from 2219 - a high strength aluminium-copper alloy used for many aerospace applications. The first two, used for STS-1 and STS-2, were painted white to protect the tanks from ultraviolet light during the extended time that the shuttle spends on the launch pad prior to launch.[6] Because this did not turn out to be a problem and in order to reduce weight, Lockheed Martin ceased painting the external tanks beginning with STS-3, leaving the rust-colored spray-on insulation bare, saving approximately 272 kg (600 lb) of weight.[7]