C402 Captain reported a rejected take-off after aircraft control was lost during the take-off roll. After several passes on the runway with a snowplow a normal take-off was accomplished.

Narrative

While I was looking at the weather before we boarded; I was told by the ramp agent and the airport manager that this is 'typical ZZZ weather' and I need to hurry up before the visibility and the weather drop below mins. After looking at the weather I decided it was safe enough to depart to ZZZ1. My out time was XA55 went to Runway XX for departure. I called Center on the ground to get my clearance. They gave me a 12 minute hold time so another aircraft could get in first. After they landed I asked the pilots how the weather/approach/ and runway was; they told me it was 'better than what was reported' I called Center back and got my release. I lined up on the center line and applied full power. I got to roughly 45 kts. and started to drift off center-line to the left and could not regain directional control so I quickly aborted my take-off; applied the brakes and was able regain control of the plane and I was able to safely slow the airplane down and taxi off the runway at taxiway. The plane was not damaged and I did not go off the side of the runway. The airport manager; was waiting on the ramp in the snow plow. They apologized for how the runway was and said they will make some passes on the runway before I try to depart again. I taxied back to Runway XX. Once the manager was finished with his 3-4 passes. They asked if the runway was good to depart on over the radio. I told that that the runway looks good from where I am at and I would taxi onto the runway and give a final word if I thought it was good. Once I got on center line I noticed the runway was good for another departure. I advanced the throttles and started my take-off. I was able to stay on center line and got to my rotation speed and lifted off without another incident. I was able to get to ZZZ1 safely and without other incident.