dismal rosemary

We finally got a bit of snow (and a big storm predicted this weekend). I still have the mock strawberry plants in the coldhouse, and they're doing grand. My rosemary on the other hand, seems to have suffered. I was bringing it in overnight and only putting it out in the coldhouse on mild days, for more sun. Must have brought it in too late one night, or it got a draft from sitting on the floor (sun spot in the house is near sliding glass door). All of a sudden it looks dessicated.

There are a few stems still green at their base, so at first I thought I could cut it back and save it. But looking at the closeup picture it looks like a bad case of spider mites. Or could just be frost damage, I don't know. I expect it might die.