Student Pilot flying C-172 aircraft reported runway excursion on takeoff roll due to ice on runway.

Narrative

I arrived at the airport at approximately XA:00 to pre-flight the aircraft and take it out for some solo work. My check ride is approaching and I planned on staying in the pattern and doing takeoffs and landings. It had snowed the night before; and there was some fog over the airport; so I performed a full pre-flight and taxied the aircraft over to the FBO on the field to wait for the fog to clear. The fog lifted fully around XB:15; and I had been speaking with my instructor who recommended practicing short/soft field landings for my upcoming check ride. I contacted ground for taxi clearance to the active runway. Another aircraft called ground immediately after me requesting taxi. Tower then called out both our tail numbers to warn us of possible ice on the apron. I taxied to the run-up area and performed a full run-up. I prepped the aircraft for a short field takeoff (flaps; elevator); called tower for clearance; and upon getting cleared for takeoff began rolling out on to the runway. I got on center-line; added power; and started moving; holding the nose off; and adding right rudder to maintain center-line. As I approached about 50 MPH; the aircraft slipped horizontally to the left. There was no abrupt turn or change in attitude; the aircraft slid horizontally. I believe I hit black ice and the plane slipped towards the left edge of the runway. Upon feeling the slip; I immediately chopped power as I did not seem to have traction on the runway; and the aircraft continued sliding sideways; eventually ending up rolling into the snow in the grassy area between the runway and the taxiway. Tower confirmed audibly what I had experienced: the plane was rotating on center-line; moving forward; then had 'apparent slippage' off to the left. The plane was towed out of the snow by FBO staff; and was subsequently inspected by our mechanic on field after the incident; and was found to be in excellent condition. No damage to any part of the aircraft; no bald spots on the tires; no excess wear. This was a very sobering experience. In the future; I will likely wait some time after a snowstorm to ensure that runway surfaces are completely dry and clear of ice or slippery conditions. My best guess is the reduced traction with the nose wheel off the ground; the left turning tendencies of the plane; developing lift taking weight off the rear wheels; along with a runway that may not have been 100% clear of ice and slippery conditions all contributed to this incident occurring.