A B737-300 CAPTAIN DESCRIBES EFFORTS TO STEER ACFT WITH THE NOSEWHEEL TILLER AFTER LANDING DURING FREEZING PRECIPITATION AND SNOW. ACFT REQUIRED TOW INTO GATE FROM TAXIWAY.

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AFTER LNDG ON RWY 4 AT ZZZ IN FREEZING PRECIP AND SNOW; I STARTED TO TURN OFF THE RWY AT TXWY P. NEAR 30 DEGS INTO THE 90 DEG TURN; I COULD NOT TURN THE NOSEWHEEL TILLER ANY FURTHER. I WAS ABLE TO CONTINUE THE TURN WITH DIFFERENTIAL BRAKING AND STOPPED STRAIGHT AHEAD ON TXWY P. I ATTEMPTED TO TURN THE TILLER TO THE L AND COULD ONLY TURN IT 15 DEGS PAST THE CTR AND TO THE R ONLY 25 DEGS. THE FO CONTACTED STATION AND HAD A TUG AND MECHS COME OUT TO THE PLANE. THE MECHS LOOKED AT THE NOSE GEAR AND NOTED A BUILD-UP OF ICE; BUT NOTHING IN THEIR OPINION THAT SHOULD STOP THE HYD SYS FROM TURNING THE NOSEWHEEL. WE WERE TUGGED INTO THE GATE WITHOUT ANY INCIDENT. SUPPLEMENTAL INFO FROM ACN 765488: AFTER LNDG; CAPT SLOWED THE ACFT AND BEGAN TO TURN OFF THE RWY. NOSEWHEEL STEERING GOT JAMMED. TILLER WAS DIFFICULT TO TURN AND HE HAD TO USE MAX EFFORT TO GET A SLIGHT TURN. USED DIFFERENTIAL BRAKING TO MAKE TURN OFF THE RWY. ONCE WE GOT STRAIGHTENED OUT ON TXWY; WE STOPPED THE ACFT; HAD MAINT INSPECT THE GEAR; AND THEY DETERMINED WE HAD TO BE TOWED IN. CALLBACK CONVERSATION WITH RPTR ACN 765485 REVEALED THE FOLLOWING INFO: REPORTER STATED ICING CONDITIONS EXISTED ON APPROACH AND DUE TO WEATHER AND APPROACH REQUIREMENTS; HE DROPPED THE LANDING GEAR AT APPROX 3000 FT AGL; WHEN NORMALLY THEY WOULD DO SO AT APPROX 1500 FT AGL. LIGHT SNOW AND SNOW PELLETS WERE ENCOUNTERED WITH OUTSIDE TEMPS AT 2 DEGS F.