Not to worry. It will probably send up new canes from the graft. Also, if you can get that last existing cane as horizontal as possible it will send up laterals off of that that will bloom this year. For future reference, never take off more that 1/2 to 1/3 of the oldest canes in any one year. And any dead wood, of course. So if you only have 3 canes only take one off. But you really don't need to take any off if the rose is still young and the canes are healthy. That's more for very old climbers that might need rejuvenation.

We, here in Ontario, are forever reminded of how B.C. has no snow....you don't have to shovel rain. But, while snow is not thought of as something to admire---many people do wait for it and cant wait to get to the slopes...B.C. knows all about that what with Whistler raking in all the tourist dollars. Roses anywhere, everywhere, have common problems, from disease to winds, especially winter winds, that can dry out a plant in no time. So do put up a barrier to how winds might confront your rose bush. So too can winds dry out the soil--so make sure the plant goes into winter with lots of water--but not too much, roses don't like wet feet. Mound the plants up at least 12" with what you feel proper....soil, leaves, boughs...and don't remove the protection until all chance of frost has passed in the spring. Don't get antsy about a spell of warm weather in March which turns nasty again and have your plants succumb to the weather. Make sure the canes are tied together securely and to the trellis, post or fence you have them on. In the spring, separate the canes by how your hand and fingers are splayed out. That is how you want to have the canes grow and gives the best chance of sunlight to all parts of the plant. Don't do major pruning at this time --remove what is weak or damaged but otherwise, leave pruning for the spring. Open wounds on ends of canes can invite disease and freezes.

The old cane stubs, if they are healthy and alive, can produce some good new canes if there are some live leaf buds present on the cane. If they are diseased with blackened areas, or are completely dead (brown all the way through) it is better to remove them. If the cane is healthy, no need to shorten. Roses store carbohydrates in their canes, so when you remove cane, you are removing stored energy. To encourage new main cane growth, regular water and fertilizer. A fluffy mulch around the plant but not in direct contact with the base helps to retain moisture and keep the soil cooler. Roses like their roots kept cool. Make sure the plant is not engulfed in weeds and make sure it's getting enough direct sun (6 hours+/day). In some soils a few tablespoons of Epsom salts (which provide magnesium) in springtime can be helpful, but be aware for Epsom salts MORE IS NOT better--you can poison the plant with too much. Measure the amount and DO NOT overdo Epsom salts.

Hopefully my attempt to add photos will help. One is of the portion of the cane that I cut off, and the other is the only bud on the cane. I checked out the link that clairegrosh provided but it seems like each section needs to be longer than mine are, and it didn't say whether I could root the whole thing. Any other clarifications or ideas would be greatly appreciated.