I have a Lonicera 'Major Wheeler' covering a small wood trellis which has bent sideways since the storm Sandy.
Dear Gardener: You can prune Lonicera 'Major Wheeler' hard so that you can replace your trellis. It will regrow, but I would not prune it to the ground, but leave 18"-24" or so for the new shoots to emerge. You should be able to redo the trellis with 18-24" of plant remaining.
As to when to prune, you should be okay as pruning around mid-October is usually safe and will not produce new growth that does not have time to harden off before winter.