Up here in Sacramento my [unprotected] Blue Java gets clobbered by frost over the winter but the corms have always survived (under a pile of mulch).
A little further to the North, but around 100' higher elevation, the "same" Blue Javas I planted in my buddy's back yard have always wintered over just fine, without any extra protection (not even mulch).
His is next to a big in-ground pool though, under a canopy of large ancient live oak so between the higher elevation + enhanced "microclimate", his thrive w/o any over-winter protection, often getting through the winter with little or no frost damage.
How your situation translates with your local conditions may be hard to figure out without actually letting them go through a few winters.
If you do decide to cut a pup off, I'd dust both cut surfaces with fungicide or at the least a rooting hormone w/fungicide added & not backfill the affected area 'till it has had a chance to scab over, in the open air & without any extra water.
I give my cut pups the same treatment (air dry the cut) for at least a week before potting them up in a very fast draining soil mix, water sparingly 'till new growth appears (couple-few weeks) & rarely lose any to rot.
Pretty much the same technique you'd use on a cactus cutting.
