Evacuation in winter is possible, the Americans do it if there is a real emergency - it's just that it's very very expensive (even for the US). Because it's possible but expensive, all the non-US bases treat it as prohibitive and effectively not to be counted on.
It's only possible in some places, for example Kerguelen island has no airstrip, the closest airstrip being on Réunion island 3000km away (Davis station on the Antarctic continent is closer, 2000km, but does not have a permanent airstrip).
No helicopter in the world has such a range, so the only means of evacuating is by ship, with the fastest ships in the area taking minimum 3 days to make the trip. If a navy ship is around, it could probably treat the emergency on board but most others will have to get back to Réunion first.
In the likely event that no ship from the French navy is around, the fastest means of evacuating will be requisitioning a nearby fishing ship but those will probably not make it to Réunion until at least one week.
Fortunately, the relative emergencies (but not life threatening) I have witnessed have always happened when a ship was already on its way for other reasons, but US or not there are real technical impossibilities in these places.
There is only the ocean along the way though, I don't think it would be possible to drop resupply fuel that way.
Aerial refueling though I guess could work, although I suspect that no suitable tanker airplane is to be found within range anyway most of the time (and no suitable helicopter either) as the military base on Réunion is not a major air force base and there is no other country than France with decent forces in the area. Australia has tankers but they're on the wrong side of their country, nowhere near Perth.
I think we're getting beyond very, very expensive here and into the territory of things no country would do outside of extraordinary circumstances, the kind of circumstances in which the country operating the base would not matter anyway as most others would cooperate in any way they could.
