How cold are your winter temperatures?
(There's an almanac function on weather underground (linked below) you tell them your zipcode and they give you data from a nearby weather station for last year, averages, and extremes.)
Are your HTs on Fortuniana, on Dr. Huey, on multiflora or own root?
Do you follow a fungicide spray program and have you been watering and how late did you fertilize?

Can you tell from the above that one answer never fits all?

Here is a link that might be useful: Weather underground portal

In my case, I don't prune until late winter (late March) and I mulch whenever I get the chance (sometimes the ground doesn't freeze until February, and I'm not going out to mulch then).

HI, ditto what Diane said. In my zone I don't prune till late March before new growth starts. Mulch ?? I only put down new mulch in spring.

We prune in later winter. We top in the fall to protect from excessive swaying from winter gales or to allow for winter protection. Which are you asking about?

Like the above I cut off the long growth in December so it won't rock the bush and break off small roots. Then I do my pruning in March to April. Just watch the temps! Remember TBEF!!!