Air Carrier Captain reported it would be beneficial to have raised lighting and chart the non-movement area at DLH airport.

Narrative

We landed in Duluth after a 15 hour duty day. It was snowing and we touched down on Runway 27. Air Traffic Control told us to roll all the way down the runway to the end and exit on Taxiway A5 and proceed into the ramp. I would estimate there was one inch of snow on all the taxiways. We exited the runway on A5 as instructed and we saw the Ramp Crew start marshalling us into the gate. We followed the Marshaller's instructions and as we were coming in I noticed a blue (in ground) taxiway light behind us as we got closer to the gate. We pulled into the gate and parked the aircraft without incident. We went and talked to the Marshalling Crew to see what the blue in ground light was. They told us there was a green painted concrete non movement area that they called 'the island' out there that was also outlined with blue in ground lights that were flush with the concrete. We figured out that we taxied over part of this non movement painted concrete area while we were following the Marshaller's instructions into the gate. The blue in ground lights and paint were covered with snow which made them non visible to us. After we taxied in further the thrust had blown the snow off the in ground lights that outlined the area which is why we saw the one blue in ground light after we had passed the concrete painted non movement area. The Marshalling Crew advised that it was not a problem that we taxied over the area as they said; 'it happens all the time.' We discussed with the Marshalling Crew how the lights and paint are not visible in snow and to take that into consideration when they marshal future aircraft into that gate because we should not be taxiing over that area.The cause of this event was snow that covered the blue in ground lights and paint of the non movement area which caused us to not know it was there till after we were past it. Also a contributing factor was the Marshaller giving us marshalling instructions that took us over part of the painted concrete non movement area. Lastly; ATC not advising us there was a non movement area when they instructed us to taxi A5 to the gate.To avoid this in the future there should be a note on the taxi chart that tells the flight crew that there is a non movement concrete island outside of the end gate. This would give crew situational awareness at night time and snowy conditions when the markings and lights are covered by snow. Also having standard taxiway edge lights that stick out of the ground would help instead of flush with the concrete so snow could not cover the edge lights of this painted concrete non movement island.