Ships could only access Kongsfjorden and Ny Alesund in the summer when there was nearly 24 hour daylight. While some winters coal mining continued and coal was stockpiled, it is unlikely that the railroad operated then. So probably little need for head lights. Besides, European railroads seemed to shun head lights for some hard to understand reason. Engines carried marker lamps so that they could be seen, but these lamps did not illuminate the track, and I think that this is still the situation today.
Here is one example in Germany on one of the last steam locomotives built - there are three marker lamps but no headlamps. This is of course in complete contrast to the USA. My dad used to complain that when driving from El Paso to Alamogordo, paralleling the SP main line, cars would dim their headlights to oncoming traffic, but trains never did and produced blinding glare for drivers.