How to Overwinter Climbing Roses
Climbing roses (hybrid tea climbers) are quite tender and there are usually only two varieties considered reasonably hardy into a cold USDA 5 ('Blaze' and 'New Dawn').
Once you get into a true zone 5, then the range of varieties grows.
If you live in a USDA zone 4 you are well advised to either grow northern type roses such as the Explorer Series or some of the hardy bush type roses.
But assuming you've grown climbing roses successfully, (and this simply takes copious amounts of compost and regular pruning) you'll come to overwintering your rose.
If you live in a zone 6, then you can simply put on your sleeping cap and go to bed for the winter. Other colder gardens have several different choices to protect this rose.
What Dies Off in Climbing Roses
Remember it is usually two things that die in climbing roses.
The first is the more tender tea rose shoots that are above ground. Unprotected, these will be killed right back to the equally tender bud union or graft. Killing either the rose shoots or the bud union or graft is a sentence of death so both must be protected.
Rose 'Blaze' one of the hardier of Hybrid Tea Climbers - if you can't grow this one, grow Explorer Roses (see above for link)
I note that many gardeners have winter kill that whacks back the tender top growth but that new growth comes from the roots. This is not the desirable rose you're trying to grow, and this rampant growth usually blooms with small pink blossoms or doesn't bloom at all. If you're unsure of your climbing rose survival, pull away the soil from around the bud union and see if the growth is above or below this point. If above, you're good. If below, you might as well dig up and toss away the rose as it is no longer the rose you planted.
Some gardeners in marginal climates pull the rose away from the wall, tie the canes upwards so the entire rose resembles a thorny post and then wrap it in flexible foam (usually available in garden shops in the fall) and cover this foam with burlap for protection. (Do not cover it with plastic)
Assuming you mound up the roots with soil and cover over the base of the foam and burlap with soil so there are no exposed roots or canes, this type of protection works quite well.
Others in colder areas will dig a trench from the base of the rose - approximately 18 inches deep and wide and as long as the rose is tall. The rose is tied upright again but this time it is dug up, tipped over and laid down into the hole. Some gardeners simply dig the trench and lay the rose over on its side by digging up half the roots (the half on the other side of the plant from the trench). With this half dug up and half still planted system, you have to be careful you truly bury the bud union and roots of the dug side. They can wind up quite shallow if you are not careful.
Online Rose Shopping
A wide variety of rose plant resources from multiple suppliers - do not buy seeds (too good to be true category)
All of Doug's Ebooks including how to grow roses in tough climates