The first does appear to be lemon thyme and the second oregano.
They are both hardy.
I have both and they've survived and thrived through 8 winters (regularly get -20 C. days and nights) and I had a lemon thyme in the north that thrived through many a -30 C. winter. My main problem with them was keeping them cut back.
If I needed the herbs during the winter I'd just dig them out of the snow.