If you're using straw it can go on anytime now; I would burlap first and stuff the top with the straw.
That self seeding rose is probably R. multiflora, a bird borne invasive, and you should root it up and kill it (It's a 99 out of 100 chance I'm right on the i.d., so I feel safe in telling you to murder that plant
You have mostly shrubs (Queen Liz is a grandiflora, a glorified tea rose really, but she's a performer, for sure), so the prognosis is good. Get a little protection on them now and you should be fine (the sheets and blankets will hold you for another week or three
Just getting some topsoil and burying the canes will work too...