I've been growing hops in half wine barrels for about 5 years. After harvest, I cut the vines to an inch or so, and cover with some leaves from the yard as a mulch.
It's worked great, and this year I had to pull root-balls and trim lots of rhizomes. Probably should have done it last year, as they were all quite root bound. But they grew grew great last year. It will be interesting to see how they do the first year after chopping up the root-balls.
It should be noted that I live in the maritime northwest, and get probably 10-15 days of sub-freezing weather at the most.