Clip off dead canes and twigs from the bottom of the climbing roses where they branch out. This is called the bud union. Cut at a joint or just past it. Trim off branches growing below the bud union as well, even if healthy. Use snips for this task.
Trim back small limbs coming off of the horizontal branches. Cut them back to a few blooms each. Use string to tie down what is left in the direction that you want it to grow. Attach the string to other branches, a trellis or fencing that the roses are growing on.
Clip off all leaves for the winter. Rake up any dead leaves around the base as well as the leaves that you clipped off. This will keep mildew and diseases at bay. Leaves that lay around at the base trap moisture and promote mold.