TRACON Controller reported an aircraft that was below the MVA; issued a climb; but could not reach the assigned altitude due to icing.

Narrative

I was working AP1 and CIC (Controller in Charge) in the tower cab with a controller who is in training; not fully certified. We were the only two controllers on duty due to COVID leave. We had adjusted the schedule in an attempt to accommodate training for the MIT with only one other CPC (Certified Professional Controller) scheduled for that shift. I had been on position for 2 HRs and 30 Minutes at the time Aircraft X called up in near the border of the 095 and 070 MVA South East of ZZZ at 5;700. The pilot was requesting vectors back to ZZZ and they were already in the clouds. The transmissions were quite. I issued an IFR clearance to ZZZ via radar vectors at 7;000 and did not issue a heading to fly. I should have issued instructions to climb to 7;000 and then issued 'Reaching 7;000 cleared to ZZZ Airport via radar vectors.' I also did not hear clearly his first transmission if he had the weather and should have issued the Runway; Wind; and Altimeter. Aircraft X was not able to reach 7;000 due to icing. I issued a suggested heading to get him to a lower MVA. Once in the lowered MVA I issued 6;000 and heading to fly. He then informed me he needed lower. I mentioned I could not give a lower altitude due to the MVA. I mentioned if he was requesting priority I could issue suggested headings and MSA from the EOVM (Emergency Obstruction Video Map) and he notified ATC. It took me a moment to be able to identify the correct altitude to issue off of the EOVM map. The altitudes listed were so small I could not read them on the scope in the Tower without zooming in the map. This was the first time I can remember having to use the map in years. Aircraft X made it back to ZZZ and landed safely. No weather depicted on the map.Recommend that we not be pushed or pressured to accomplish training on days when we are minimally staffed so that we are not on position over 2 hours. This pressure appears to be coming from above the facility level and then is manifest through management locally.I also believe it would be best to have a refresher training from outside the facility on use of the EOVM map; with a scenario on our map; to help with confidence in use when the rare occasion presents itself for its use.I appreciate the detail on our EOVM map; but would suggest that the altitudes that we should be issuing; during these types of situations; would be large enough to easily be issued without the zooming in and out.