Cessna 172 Instructor pilot reported an altitude deviation in an area of mountainous terrain during daylight visual conditions on an IFR flight plan. The pilot became distracted while avoiding icing conditions and descended below the ATC assigned minimum enroute altitude; then recovered and continued the flight.

Narrative

I was on a commercial duties of PIC (pilot in command) training flight with a student in day VFR conditions under an IFR flight plan. We were maintaining 9000 ft. MSL. A cloud layer ahead of us (9000 ft. MSL-12000 ft. MSL) posed a threat of icing due to the noted OAT at that altitude (1 deg C). We requested to divert off route to the right heading 120. ATC gave it to us. It was apparent after a while that we would not be able to maintain cloud separation unless we descended. We ultimately requested to descend to 7000 ft. MSL. The idea was that we would maintain clear of clouds and be in temperatures above freezing. They cleared us to 8000 ft. MSL. We overshot and descended to roughly 7650 ft. MSL. ATC notified us of the altitude slip and we made immediate corrections. We climbed at best rate with full power; but were unable to get back to our assigned altitude promptly. ATC informed us of a possible pilot deviation moments later due to the altitude deviation which caused us to descend below the MEA. The cause of this deviation in my opinion was fixation. I was fixated on remaining clear of icing conditions and altitude was an after thought; despite being on an IFR flight plan.