This video from the Antarctic says about itself:
That Incredible Little Arctic Tern
Feb 13, 2013
We went to Antarctica to see the penguins, and we certainly did. But we saw so much more wildlife: orcas and elephant seals and leopard seals and many different seabirds. My favorite is the Arctic tern, a little bird that migrates further every year than any other in the world… from the Antarctic to the Arctic, and back – 20,000 miles every year.
Spitsbergen, 7 June 2013. After the black guillemots of the sea near the mouth of the river of Bjørndalen valley, we go to the east. More Arctic terns have arrived from their long journey from the Antarctic, to near the artificial islets, made especially for them here.
We pass Longyearbyen, and go further east: to where we have seen the lone pectoral sandpiper in the Adventdalen valley.
The male pectoral sandpiper is still doing his courtship flights, with their U-u-u sound. Still, no pectoral sandpiper female.
Not far away, a snow bunting couple. Again and again, they fly to where they are very probably building a nest.
The book Birds and Mammals of Svalbard says about snow buntings:
They usually place the nest in rocky crevices, under rock slabs, in screes or in buildings, well out of sight. Snow buntings will also use artificial nest boxes.
Where this couple are building their nest is obviously artificial. It is a wooden box with rocks inside it. But, did people put this box and these rocks here to help nesting snow buntings?
This big wooden box here with rocks certainly looks different from this snow bunting nest box from the USA (see also here). On the other hand, it does look similar to natural nest spots for this species.
Here is a video of a snow bunting in yet another type of nest box, also different from what we saw in Adventdalen.
The Alaska Department of Fish and Game writes:
Snow Bunting nest boxes can be placed almost anywhere in tundra habitats. Snow Buntings will nest in boxes on the ground, on posts, or on a house in alpine, wet or moist tundra areas. However, nest boxes on the ground may allow easy access to predators.
Both in natural nests and in nest boxes in Svalbard, snow buntings may have parasites: mites of the species Dermanyssus hirundinis. These mites are adapted to Arctic weather. Svalbard is the northernmost place where they have been found.
How does climate change affect Svalbard snow buntings? See here.
The female snow bunting builds the nest.
Birds and Mammals of Svalbard says:
The nest is built mainly by the female.
David Freedland Parmelee writes:
The female snow bunting builds the nest alone, though the male often accompanies her to and from the nest site and occasionally even picks up nesting material and offers it to her.
We saw both the male and female repeatedly flying to the probable nest spot. Maybe this couple, or the relatively short time of our observations, was not representative of the species.
Not only the snow buntings were present. A reindeer was there as well.
And dunlins. Sometimes up in the air, in a courtship display flight.
And sometimes on the marshy tundra floor or in a puddle, looking for food.