It's perfectly acceptable to care obsessively for the little good that we have!
Personally I wear a cheaper and more disposable (than "my first good pair") headphone whenever I am to expose them to the sun, wind (dust, pollen), snow/water, cold... and blood (when I'm fighting wild animals in the forest).
I use my very best only inside and away from direct sunlight... replace them inside their dust-proof case between use, etc.
But I have ranks and a different headphone for every purpose really, so music is accessible at all time.
I'm only telling you what I do, sorry if that's not helpful and you really want to wear your UE6000 outside, lol.
I would guess it would okay, as long as you make sure water doesn't get inside the cups inside the drivers. Maybe you could wear a hood when it's snowing directly on your head to be safe.