My arugula patches have sailed through the winter, so far, both here in the Piedmont and in the mountains. Of course, the winter has been mild! (It was 70° F this afternoon - peculiar).
I had the idea that arugula's frost tolerance was more like "normal" lettuce (not Winter Density or North Pole or Arctic King), and so it's been a revelation to have these flourishing patches -- happily, it's the one "green" (along with cilantro) that deer haven't eaten in the satellite garden (in the Piedmont).
It's a bit discouraging to think I'll need to fence/protect/defend my less 'spicy' greens from deer, if I want to grow them. Kale, lettuce, spinach, broccoli, collards, etc. have all disappeared as deer forage over the last few cool-weather seasons. Even French sorrel -- yikes.
Happily, in the mountains, my raised beds are in front of the house, and I don't think we have deer (yet), and only very brave woodchucks venture that far out of the woodland ravine behind the house (in dry summers, primarily).