Well, that depends--
Folks in areas where it's wet in the winter and it doesn't freeze generally clean them up to avoid rot issues over the winter.
I'm just to the west of you in Utah (on the other side of that mountain) and I might pick at a few in the fall just for aesthetics, but I do not clean them up in the fall because they do just fine with their own dead leaves here (I do clean up all the dead leaves of the trees and other plants off of them so they don't get smothered).
In dry winters, I think it helps them to have their dead leaves... and when tempted to feel neglectful, I remind myself that there are probably no little fairies with tweezers cleaning up the ones clinging to life in the Alps in preparation for winter...just the bugs and although they do not do as good of a job as the tweezer-fairies, they do alright
But if you want to clean them up and tuck 'em in with gravel or grit, I'm sure they won't mind