A B737 flight crew suffered the loss of pitch trim during and arrival and landing in heavy precipitation and icing.

Narrative

Following the disengagement of autopilot/auto throttles on final approach; (aircraft configuration was Flaps 10; landing gear retracted) I called for the landing gear down; Flaps 15. I noted while the aircraft configuration was changing; the electric trim switch on the First Officer's control column didn't work. Brought it to the Captain's attention and asked him to try his trim switches. They; too; did not work. At this time we were in VMC conditions; with heavy winds (45-65 KTS from the southwest); and felt the conditions were deteriorating. (On the initial phase of the approach we encountered icing and heavy precipitation; with reports of moderate turbulence). We identified the problem as an electric stab trim fail. Once the aircraft was fully configured; and inside the FAF; I noted the trim position was about 6 degrees nose-up; which was consistent with our weight and configuration; and would require some forward pressure on the yoke should a go-around be required; but would be fully controllable. In final configuration the aircraft remained in a balance and trimmed state for an uneventful landing and rollout. Following block-in when the power had been shifted to ground power I noted that the electric trim operated. I'm not sure if this was due to the power source shift; or whether icing encountered on the approach had affected the trim motor.