PA-28 flight instructor reported encountering unexpected icing during IFR training flight.

Narrative:

Filed IFR for an instrument training flight. During weather briefing no reports of icing or potential icing were seen on 1800wxbrief.com. Departed from ZZZ in VMC conditions; but entered IMC at cruising altitude of 4;000 feet MSL. Temperature at 4;000 feet was +2 degrees C. The winds aloft; checked via adds (aviation digital data service); had forecast +2 degrees C up to 6;000 feet. Descending into destination airport (cxy) started picking up ice after descending through 3;000 feet while being vectored for the ILS approach to runway 8 at cxy. Despite defrost being set at max; the windshield iced over. Approaching minimums I was focused on trying to sight the runway and approach lights and my student diverted his attention from the ILS display to the windshield as well; resulting in a low altitude alert from the control tower. While descending through 1;000 feet MSL the ice began melting. Surface temperature was +1 degrees C. As there was an apparent temperature inversion; decided to check latest weather via adds and saw that temperature at cxy and at planned [cruising] altitude (5;000 feet MSL) was positive. Conducted return flight to ZZZ and briefly picked up light icing while climbing through 2;000-3;000 feet. At cruise altitude OAT showed +2 degrees and there was no icing for the return flight beyond the climb-out phase.

Original NASA ASRS Text

Title: PA-28 flight instructor reported encountering unexpected icing during IFR training flight.

Narrative: Filed IFR for an instrument training flight. During weather briefing no reports of icing or potential icing were seen on 1800wxbrief.com. Departed from ZZZ in VMC conditions; but entered IMC at cruising altitude of 4;000 feet MSL. Temperature at 4;000 feet was +2 degrees C. The winds aloft; checked via ADDS (Aviation Digital Data Service); had forecast +2 degrees C up to 6;000 feet. Descending into destination airport (CXY) started picking up ice after descending through 3;000 feet while being vectored for the ILS approach to Runway 8 at CXY. Despite defrost being set at max; the windshield iced over. Approaching minimums I was focused on trying to sight the runway and approach lights and my student diverted his attention from the ILS display to the windshield as well; resulting in a low altitude alert from the Control Tower. While descending through 1;000 feet MSL the ice began melting. Surface temperature was +1 degrees C. As there was an apparent temperature inversion; decided to check latest weather via ADDS and saw that temperature at CXY and at planned [cruising] altitude (5;000 feet MSL) was positive. Conducted return flight to ZZZ and briefly picked up light icing while climbing through 2;000-3;000 feet. At cruise altitude OAT showed +2 degrees and there was no icing for the return flight beyond the climb-out phase.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.

Attributes
ACN	1622053
Time
Date	201902
Local Time Of Day	1201-1800
Place
Locale Reference	CXY.Airport
State Reference	PA
Environment
Flight Conditions	IMC
Light	Dusk
Aircraft 1
Make Model Name	PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Operating Under FAR Part	Part 91
Flight Phase	Final Approach
Flight Plan	IFR
Person 1
Function	Instructor Pilot Not Flying
Qualification	Flight Crew Air Transport Pilot (ATP) Flight Crew Flight Instructor Flight Crew Instrument Flight Crew Multiengine
Experience	Air Traffic Control Military 2 Flight Crew Last 90 Days 120 Flight Crew Total 10300 Flight Crew Type 2000
Events
Anomaly	Inflight Event / Encounter CFTT / CFIT Inflight Event / Encounter Weather / Turbulence