On February 24, 1998, at 1141 hours Pacific standard time, the airline transport pilot of a Beech BE99, N20FW, encountered elevator control problems and landed safely at his destination. There was no aircraft damage or injury to the pilot, the sole occupant. The flight departed from Burbank, California, on a 14 CFR Part 135 air cargo flight to Oakland, California, and was being operated by Ameriflight, Incorporated, on an instrument flight plan. Visual meteorological conditions prevailed for the landing site. During a postflight inspection, ice was observed in the tail section of the fuselage in an area that surrounded the elevator control cables. The "limbers" and water drain hole that evacuate this area were found clogged with small "fuzz-like" fibers. (See the sketch in Section 10.00 attached to this report.)