B737 Captain reported during descent they got a master caution for the number two engine cowl anti-ice. They descended below icing conditions and landed.

Narrative

While descending through FL270 on the ZZZZZ arrival into ZZZ; the master caution light illuminated with an anti-ice amplifier. The overhead panel indicated a number 2 engine amber COWL ANTI-ICE indication. In conjunction with the First Officer; we completed the QRH actions to include reducing the thrust lever (affected engine) until the COWL ANTI-ICE amber light extinguished. The throttle reduced to idle and the light remained on so we left the throttle at idle to troubleshoot. Note that the Master Caution light and amber COWL ANTI-ICE lights periodically flashed/flickered with no noticeable connection to throttle position. While completing the QRH items; I coordinated a level off at 250 to remain VMC and received a clearance to hold at ZZZZZ1 while troubleshooting. After completing QRH items and entering the holding pattern; Dispatch was notified and a patch to Maintenance Control was initiated via VHF. After a discussion it was agreed that anti-ice would not be reliable so flying in icing conditions would be unsafe. The OAT indicated -10 with clouds; rain and embedded thunderstorms between our current position and ZZZ. The plan agreed upon by the crew; Dispatch; and Maintenance Control was that we would descend in holding to below icing conditions and proceed to ZZZ as planned with the number 2 engine at idle understanding that the engine was available if we needed it. It was also decided that we would use the engine once established on the approach for the final descent to the runway. The plan was executed as briefed with no further incidents. The amber COWL ANTI-ICE light remained illuminated until we brought the number two engine up for the approach around 3000 feet at which point it extinguished for the duration of the flight.