Air Traffic Controller reported aircraft on departure returned to the airport due to severe smoke in the cockpit.

Narrative

There was about 1/4 mile of visibility with a snow squall coming through. We were in a formal deicing program. I cleared Aircraft X for takeoff and before the aircraft came up on radar the pilot stated that they were returning for landing due to severe smoke in the cockpit. I observed the aircraft making a sharp left turn and the altitude indication 003 on radar. I could not see them out the window due to the ceiling and visability. I cleared them to land runway XX. At this time the pilot came over frequency frantically yelling 'climb climb climb'. The target was no longer depicted on radar meaning they had dropped below 200 feet. At this time I cleared the aircraft to land on every runway we have at ZZZ airport. Whatever they needed. They were able to climb back to 300 feet. The aircraft overshot runway XX and coming around for runway XY. I attempted to give the pilot a visual of runway XY as I saw the tag approaching it; they were not able to find it and overshot it again.They asked for vectors for runway XZ or runway XY at this time. They were at 300 feet still. Minimum vectoring altitude is 1800 feet due to terrain and obstruction. I asked if they could climb and they were able to get up to 1500 but no higher. I issued a heading that was obtained from ZZZ approach control told them to maintain 1500 and switched them to ZZZ approach. ZZZ approach then set them back up for final for runway XZ where they safely landed.