Cessna 402C Captain reported a taxiway excursion resulting in a damaged propeller during taxi. Captain shut down both engines.

Narrative

During the taxi out to runway XX; I had started on Taxiway 1 and then made a right turn on taxiway 2. Taxiway 2 was completed covered with compacted snow and ice covering the asphalt. Visibility was low since it was night and there is very little lighting in the area; however I did have the airport tax lights on along with my headlight and landing lights for the duration of the taxi process. Upon making the right turn onto 2; I thought I was following a centerline down the taxi way; but eventually realized that the aircraft had drifted to the left and my left tire; and now main nosewheel tire; were in the snow bank to the left of the taxiway. Once realizing that the plane was off 2; I immediately shut down my left and then right engines and called the FBO and operations for help. Upon exiting the aircraft; based on the tire tracks; I had been in the snow bank for approximately 100' following the 'false' centerline even though I had appeared to be well within the mid point of the blue airport tax lights. Additionally; after inspecting the left propeller; it had struck one of the airport taxi lights and had damaged two of the three blades.Cause: The reason for drifting off the taxiway was due to the poor conditions of the taxiway. There was compacted snow and ice covering the entire length of the taxiway making the centerline and any additional signate not visible.Suggestions: The runway and all taxiways at this airport need to be better cleared for better visibility. Perhaps taxi centerline added to due to the volume of snow and ice received at this airport on such a regular basis.