General aviation instructor reported observing their student pilot exited the runway at a higher speed during their solo flight; resulting in a taxiway excursion. No injuries or damage occurred.

Narrative

Student was sent on her first solo after completing 3 landings with me; her instructor; and they were all good. On her solo flight she completed one landing and taxied back. On her second landing she was taking the turn-off too fast and went slightly into the snow on the side of the taxiway. She was able to shut down the plane. I had asked her what she thought happened - she said she didn't feel like she was going too fast around the turn. I was up in the tower watching her and did notice she was taxing faster than usual; probably due to nerves. No damage to propeller was evident upon initial visual inspection. No injuries. We debriefed after the flight and talked about lessons learned.