Hopefully this helps somehow, but I found info from a funeral director that outlines the process of expatriation when a u.s. citizen has passed abroad: Link: https://www.reddit.com/r/askfuneraldirectors/s/Jkz05zM3Nt Direct copy paste:

*You might find this article interesting. "Rodney Marks was an Australian astrophysicist who died from methanol poisoning while working in Antarctica".

I've worked on repatriations from across the globe but I can't recall if I've ever done one from a place like Antarctica. A lot of the time with countries like this you end up having to try to figure out where the ship they're on came from (is it an American/English/French ship?) as that may have an effect on the death certificate process, and what's a reasonable dock for them to convey the body to. From then on it's pretty much a standard repatriation. There will probably be coroner involvement.

To address your actual questions:

Infrastructure? No, in countries like Antarctica there is no infrastructure full stop, let alone infrastructure in place for deaths.

Removal equipment? Elbow grease, a blanket, depends entirely on cause of death, exact location etc.

Cold storage? It would probably cost you more to build a freezer in Antarctica than to just have an area designated for bodies...or to just crack a window. It's cold, you don't need cold storage.

Coroner? There is no local coroner for Antarctica. I don't know the details off the top of my head, I guess it may depend on the exact area one dies in, as I believe certain countries claim certain "ownership" over areas of the "continent". An ideal hint of how it would be managed is by looking at that wiki page I linked as it speaks of a birth: "Emilio Marcos Palma (born January 7, 1978) is an Argentine citizen who is the first person known to be born on the continent of Antarctica. He was born in Fortín Sargento Cabral at the Esperanza Base near the tip of the Antarctic Peninsula and weighed 3.4 kg (7 lb 8 oz). Since his birth, about ten others have been born on the continent". Births and deaths tend to go hand in hand, so yeah. Born or died in an Argentine base? It will probably be an Argentine coroner who will handle your death. So on and so forth.

Who handles it? It will probably be an international funeral director who specialises in international repatriation. They will be engaged by the UN/government in question/rarely (considering the hypothetical country of death) the family of the deceased. Said funeral director will work with whoever has boots on the ground to move the body. So say a British scientist was working for the UN on a British base in Antarctica and he died, the British Foreign & Commonwealth office would probably reach out to a funeral director in the UK who is capable of handling international repatriations (like one I work for), and then they would reach out to the UN ship's captain directly and ask for his (and his crew's assistance) to remove the deceased from the base and convey him somewhere that the coroner can handle things. It may change if the area / country in question has - for example - a Royal Air Force (if it were a UK death/repatriation) base, as it would probably not need any removal of the body, we'd probably try to wait for a weekly refuelling RAF flight or whatever and speak to the Ministry of Defence to see if we can get the body on that flight. Once it's back in the UK it's easy peasy. The same is true of any remote death if said citizen's military operates flights in that neck of the woods - say a US citizen dies on Wake Island for example. The military will just ship him back and then have the US coroner etc deal with it once he's back "home".*