Here we go!

I went skiing at the Cortina Ski Resort in 2008. I just examined the Dolomites WHS map carefully, and found out that Cortina was not even in the buffer zone. I have not examined other 11 ski resorts in the Dolomites on the map, so maybe some other ski resorts are in the core zone...

I'm assuming that if a ski resort exists within the core zone of a WHS, it exists in a sustainable way. :)

I havnt checked, but from memory I think you can ski in Marmolada.

There might also be a ski resort in Laponia though unclear if in the core zone and ski resorts are often just lodges over there.

Just checked - you can ski and there are lifts in the core zone of Marmolada in the Dolomites.

It is also possible to ski - with lifts - in the buffer zone of Hallstatt-Dachstein. This is in the western, less visited, part of the site. The lift starts right on the boundary but it would be very difficult to ski into the core zone. I've mountain biked through the core zone there - it is spectacular!

Oh, I just compared the WHS map and the Marmolada piste map, too. Yes, there are at least 2 lift stations, Punta Rocca and Serauta, that are definitely in the core zone.

So,

1. Canadian Rocky Mountain Parks

2. Pyrénées - Mont Perdu

3. Dolomites

Laponia is a Nordic skiing paradise, and I've done it around Abisco, which is not part of WHS. But for Alpine skiing, I'm not sure. If there is a ski resort, it would be quite small or just some lifts, I think.

Ski sustainably!

In Hallstatt-Dachstein there is also a ski area (with ski lifts) within the core zone, see the map on this website:

https://www.derdachstein.at/en

The main ski area is the "Schladminger Gletscher", which is labelled on the map with "Cross Country Skiing" and Alpine Skiing". It is best reached by gondola from the south side of the WHS. You cannot get there from Hallstatt without hiking.
The boundaries of the core zone run along the mountain ridge.

I was thinking of Zwieselalm - the core zone boundary passes next to the z1 lift, it is only in the buffer zone.

However; there is also Dachstein Krippenstein (with lifts) in the core zone!

So the Hallstatt-Dachstein WHS has two different ski areas within its core zone.

Banff NP at the Canadian Rocky Mountain Parks WHS has actually 3 ski resorts within itself (Lake Louise, Norquay, and Sunshine Village), although I haven't checked if all of them are in the core zone.

To think about it, when I went to visit an ice cave at the Hallstatt-Dachstein WHS, I took cable cars all the way to the top afterward. It was in summer, but I guess that's where they ski in winter.

Pontoons in the core zones

By pontoons I mean those stations docked but floating in the sea. They can be used as a platform to go snorkeling or scuba diving, but they are for everybody and often come with glass-bottom area, through which you can see sea life. Boats can dock at Pontoons, but even helicopters can land at those with helipads. In this sense it's like the International Space Station in the sea. (Or the International Space Station is like a pontoon in the space.)

Obviously, I have not been to too many WHSs with diving spots, and I have seen these pontoons only at the Great Barrier Reef in Australia and Punta Cana in Dominican Republic, from which I went scuba diving, but the latter is not even a WHS.

For the purpose of this post I will include pontoon boats at Belize Barrier Reef WHS.

1 Great Barrier Reef

2 Belize Barrier Reef

3 ???