I would personally see if I could get her out first than break her, wrong time of the year for being broody but those bantam don't seem to care. I feel guilty too, but if she doesn't have fertile eggs than it's all pointless and draining on them.
Sometimes the snow comes in sideways, we are...
If she's anything like my cochins she will sit under there for about 2 months before giving up, I might try a rake to push her off and out of that catatonic state, she should then start up a cackle and run off, if you get snow will she get buried under there?
Thankfully all my hens seem to be sensible, or at least trusting of me, they have always gone broody in the nestboxes, though I've have two in the same box arguing over the eggs and becoming co moms, your Cochin is adorable, they are one of my favorite breeds.