ABSOLUTELY!!!! Every External Tank needs insulation. If not, the cryo temps would cause awful things to happen. LH2 (liquid hydrogen) is at -432 degrees F at sea level pressure (and the Cape is most assuredly at sea level!). At those temps, air liquefies (if the two feet of iced up condensation on the outer skin does not insulate first!)!

The first two flights back in the 80's (STS-1, & -2) flew with HWT (Heavy Weight) ETs. Those two were painted white, primarily for thermal reasons (reflectance). After those first two flights, the Thermal weenies realized that we did not need the very slight benefit of the white paint (it was actually latex), and we could save 600 lbs per flight by eliminating it. So we never again painted an ET. The SOFI (Spray On Foam Insulation) that we use on the ET is a polyurethane foam, not unlike Great Stuff that we can all buy at Home Depot. When sprayed here at NASA's Michoud Assembly Facility, it is very lightly colored, almost white. The deep orange, almost brown color that you see on TV at a Shuttle launch is actually "tanned" SOFI. UV radiation causes it to tan, much like human skin, and it turns the much darker shade.