Small Transport; Low Wing; 2 Turboprop Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 10
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Weather / Turbulence
Air Traffic Control Issued New Clearance
Airspace Structure; Environment - Non Weather Related; Human Factors; Weather
Aircraft X called for clearance and release off of Runway 27 at ANE. There was a snow event in the area. There was trace icing reported at 4000 ft. I issued the clearance and release and instructed the aircraft to 'Enter controlled airspace heading 090' there was trace icing at 4000 ft. so I instructed the aircraft to maintain 3000 ft. There was an obstruction south of the ANE airport with an MVA of 3400 ft. I assumed that the aircraft would make the turn tight enough to stay north of the obstruction on the 090-degree heading. The aircraft turned wider than anticipated and entered the MVA for the obstruction. When I became aware of the situation I issued a climb to 4000 ft. I should not have assumed that the aircraft would have turned as expected and issued a heading north of the airport to avoid the obstruction or just issued 4000 ft. as an initial altitude.
TRACON Controller reported keeping an aircraft below the MVA due to icing conditions.