I landed a 737-300 at Stockholm after flying through some Sc for about 5 minutes. Can't remember the OAT but it was within the definition of icing conditions, so we selected ignition on and engine TAI. After 2-3 minutes we noticed ice building up on the wing and windshield wiper posts so we selected wing TAI as well. The wing TAI seemed to be doing its job but the ice on the windshield wiper posts was growing quite quickly. We started the APU and selected the ignition to 'Flight'.
After an uneventful landing, we were amazed during the subsequent walk-round to discover 4 inches (yes four inches) of ice all over the unprotected surfaces. These included the fin, stabiliser, engine spinners and radome. As the OAT was hovering around freezing we had the whole aircraft de-iced before we could go again.
So, the theory that the tail 'doesn't collect ice' is not borne out by my experience. What is remarkable, however, is that there were no handling or performance issues that worried us. Some time later I discovered that Boeing conducted tests using wooden shapes attached to the leading edges of the tail surfaces during certification, in order to show that TAI of these areas was not necessary.
By contrast, I seem to remember a Viscount that crashed due to a very small amount of ice on the tailplane causing flow separation when the flaps were fully lowered. Other types I've flown have AFM notes warning about similar problems but on the 737-300 that didn't seem to be an issue.
Currently on the 747-400 and that only has wing leading edges and engines de-iced as well.