Mice/moles have eaten my rhubarb!

So I uncovered my rhubarb plants this past weekend (I live in the mountains of Utah, we get extremely cold whether, so plants are protected by a thick layer of leaf mold in fall after the frosts have killed off the leaves) to discover either moles or mice have eaten the rhizome of one plant and about half of the other! Sneaky buggers. Last year was the second year for the rhubarb, and production was amazing.. so I was all set for an even larger harvest this year.
So my question.. how can I protect my plants next year? If I don't mulch, then the freezing temperatures may kill the plant (we don't always have a reliable cover of snow, as it's a semi-arid mountain desert). Obviously I'll work on the mouse/mole issue.. but I don't mind them being in the garden; or even having a nibble or two.. just not the whole plant!
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Bit of a dilemma as it sounds like a good mouse/vole house as well as good place for the rhubarb. They probably thought, 'oooh that's nice, someone built us a great house for the winter', 'Yeah, and look they left us some food too!'
Would it set the rhubarb back a lot to dig up the rhizome and store out of the ground? Not something I've ever tried, I'm only in the second year of rhubarb growing, can't even eat any of mine until next year.
I thought rhubarb was very hardy, grows in Siberia. What about pinning horticultural fleece over them? Have you ever tried not protecting them?
No, I've always protected them. It can be -28C here for a week or two on end during the winter.. and dry. The ice evaporates directly out of the soil, right from solid to gas. I know rhubarb is very hardy (zone 2, I believe.. I'm zone 5).. but the temperature under the snow is different to the temperature above ground exposed.
Sounds like time for an experiment. Maybe an upside down pot with the edges buried a bit to deter the mice (obviously they can dig under if they are determined). Or maybe I'll just leave them exposed, and keep my fingers crossed.