texas hops

so i'm in san antonio texas and have one chinook that survived a move and a couple of dogs who like to dig in my planters. its a first year and i was out ot town and not able to harvest. so here's my question. what do i do to in the winter? we get a couple of lite freezes in the winter and maybe one or two hard ones. we had an "ice storm" here that lasted 3 days several years ago that shut down the city to give you a bit of perspective. do i still cut them back and cover them with mulch? or, can i cut them back and try to let them grow throughout the season with the few bits of freezing temps not hurting them?

The bines will die regardless of what you do. Hops go dormant and won't do much until after the Spring thaw.

Chicken wire laid over the hop patch will eliminate digging.