The May-June 1962 issue of Boeing's Airliner magazine details the deactivation and removal of the 707 stabilizer ice protection system. It is quite a classic read from an icing standpoint, reflecting a number of misconceptions about icing that have since been severely challenged, such as cloud vertical extent and droplet distributions, as well as the frequency of severe encounters. However, the key statement is that during testing with a representative three inch ice shape, no changes in control forces or stability were noted. This is the most important aspect, although they then devote a lot of verbiage to things like fuel consumption and landing climb weight limits due to limited thrust in some airplanes.
The only real threat from ice on the tailplane, and it is a big one, is tailplane stall during slightly higher speed approaches with full flaps. The early stages of this threat are manifested by changes in the control balance of the elevators, resulting in stick force lightening or outright reversal. This has a devastating effect on longitudinal stability, and quickly leads to elevator snatch, driving the control column full forward with the resulting pitch down.
This problem is neatly solved with irreversible (powered) flight controls, which are quite capable of overpowering a change in elevator balance. Thus, nearly all large jets have none of this issue, ice protection notwithstanding, because the elevator can easily be re-cambered to avoid the stall. The L-1011, of course, is a different animal due to the full flying tail, but I suspect that the aerodynamic analysis required to support the operation of that design in various flap configurations probably included huge margins to deal with ice contamination.
The 707, however, does not have powered elevators, nor does the DC-8 or DC-9 and MD-80. I know little about the DC-8 beyond noting that Douglas, apparently, opted to keep their tail ice protected when Boeing dropped it. That ought to raise a red flag; the Douglas fellows probably knew something that did not encourage them to press for a similar de-activation. I do know that the DC-9/MD-80 fleet has a problem with tailplane stall, and there have been a number of incipient cases with full flaps selected. Boeing, on the other hand, had enough stall margin designed into the 707 stabilizer to preclude any issues with the tested ice shape, and there is no service history that I am aware of in the zillion or so hours it has flown. Boeing has continued to design in that stall margin on subsequent stabilizer designs, while arguing insufferably against any certification requirement to do so.