we do have on the 737 an ice detecting system,which tells when ice appears,then by another light 'no ice' tells when the ice was eliminated.
the ice detector is on the forward left fusselage,near the data probes.The detector operates by magnetostrictive oscillation (magnetically induced vibration). When ice forms on the probe, it has a different vibrational freq than when it is clean.It works only in flight.It is deiced periodically by internal heaters.
dud: that site is not entirely accurate. Also ice can form on the plane with no visible indication on the windshield.
Brgds Alex