C-172 pilot reported a runway excursion during landing rollout thought to be the result of a patch of ice with poor directional control.

Narrative

No icing reports; no runway condition reports or PIREPS that would indicate any runway contamination. The only PIREP at the time was for rime ice in the clouds. Obtained ATIS several times that morning. Called the Tower and they mentioned that snow was moving in but was not yet over the airport. I taxied to Runway XXL and also commenced a run-up. I was then cleared for take-off on Runway XXL and stayed in the left traffic pattern. Once airborne I noticed snow coming down from the clouds (virga) about 4 miles west of the airport. After 1 touch and go; I heard another airplane was cleared for take-off and they also decided to stay in the pattern. I was 'Cleared for the option' a second time while turning on downwind. Tower asked the [the other aircraft] how close the snow/virga looked. They said that it was 'pretty close'. Then the Tower amended my clearance to 'Clear to land'. At this point virga had not yet reached the airport area. At about 300 - 500 ft. after touchdown and while applying normal brake pressure the plane started to fish-tail. I took my feet off the brakes and the plane veered sharply to the left and exited the runway and onto the grass. While on the grass I was able to keep directional control with the rudder and brought the plane to a full stop. After receiving taxi clearance from the Tower I taxied on to the taxiway and back to the FBO. After parking I examined the aircraft and found no visible damage to any part of the aircraft including the propeller. I wrote up the incident on the Maintenance Squawk Sheet and then called the Tower to converse about the incident. I communicated with the maintenance department of the company that rented me the aircraft as well as their management. I have also been in contact with a person from the FAA who reached out to me after the incident. Since I didn't experience any issues with either steering or braking at any other time except at the time of the incident; I concluded that I must have hit a patch of frozen water that had not been previously reported or noticed by anyone.