It’s always hard to tell from a single image what variety a peony is, especially since there are thousands of different cultivars, of which many are understandably much alike. It’s a ‘bomb’ form with some white petals in the middle and the outer layer of petals pink. Many fit that bill, but a common one is ‘Sorbet’. I cannot find much about that peony, it’s not registered with the APS, all Google tells me is that it should be a Dutch introduction, date not really given. But it’s very easy to find, thus it must have been around for quite a long time. Simply search with Google for ‘paeonia lactiflora sorbet’ and you’ll find scores of e-shops selling it (and you can have a look at several images to compare), although it’s probably a bit late to buy it now, better wait for Fall.
I don’t think the ‘mild’ winter killed it by the way. Peonies can tolerate quite some cold, paeonia lactiflora for sure. Probably other plants overtook it’s root system and took all nutrients away or the foliage was below other plants and it simply didn’t grow very well. Anyway, I’m pretty sure they can take the cold in Switzerland (perhaps not high up in the Alps, but normal conditions shouldn’t be a problem).
All the best,