B737-700 Captain reported rejecting takeoff due to the runway conditions and its impact on the aircraft as it began to accelerate.

Narrative

[I] rejected takeoff [at] less than 80 kt. due to unstable directional control. [The] aircraft taxied down Taxiway 1; which was covered with snow; partially compacted. [The] aircraft was cleared for takeoff on Runway XXL full length. We had run performance data for windshear and briefed the precautionary windshear profile as ATIS was reporting low level windshear advisories were in effect - wind was 310/15G25. After raising the power to 40 percent N1; I pushed TO/GA and the thrust levers accelerated to max takeoff power. As soon as the aircraft started to accelerate; the aircraft started to veer to the right. I applied left rudder and the aircraft started to come back to centerline. Approaching centerline; I reduced left rudder and added right rudder; but the aircraft continued to the left through centerline and was not correcting. I made the decision to reject the takeoff at approximately 60 - 65 KIAS. As we slowed through about 20 - 30 kt. the aircraft started to slide on the runway even with full brakes applied. We stopped on the runway and then taxied clear. Total distance from brakes release to taxiing clear of the runway was approximately 2;000 ft.I thought that the nose wheel was aligned with the runway centerline; but the possibility certainly exists that it was slightly canted to the right. I underestimated the runway conditions which I feel exacerbated any misalignment that may have existed prior to takeoff power being applied.