The horizontal stabilizer's job is to counter this, by exerting downward lift and thus noseup moment. This means that if the tailplane stalls, it essentially stops making the downward lift needed to counter the nosedown moment. The aircraft may pitch down uncontrollably. Knowing that ice effectively lowers the stall angle of attack on the main wing, it's easy to see how this works on the tail, too. In fact, it's conceivable that the tailplane could have enough ice to stall it, when none is present on the wings.
Flaps aggravate the problem.
In all airplanes, flap deployment produces downwash that affects the tailplane and elevator. In some airplanes, this downwash is so pronounced that it produces a local airflow that changes the tailplane angle of attack substantially. Ice acts like a stall fence, encouraging the onset of tailplane stall. Tailplane stalls have gotten a lot of press since 1991, when NASA and the FAA conducted a conference on the topic of tailplane icing. Since then, several accidents have been directly linked to tailplane stalls and, retrospectively, other heretofore unexplained accidents may also have been the result of tailplane stalls.