Question
I have 2 New Dawn climbing roses growing over a pergola.  They were "own root" roses that are now 3 years old.  They have bloomed prolifically and been very healthy up till now.  I have one plant that now has canes that have a few leaves budding on them, but the cane itself is turns yellow and then brown and dies.  Some of the large canes look like they have a light dusting of a greenish powder on them; almost like green pollen.  I have looked all of the diseases and funguses that I could find online and do not find anything similar to what I am seeing.  So far I am cutting off the dead portions of the vine and burning them just in case they are infected with something.  None of my other rose bushes on the pergola appear to have problems but this one (I also have 2 Eden climbing roses on the pergola).  At the beginning of spring I started spraying with an insecticide/fungicide rose treatment.  I live in North Louisiana in zone 8.

Answer
If a rose cane is damaged by hitting with a hoe, pruning, wind or thorns rubbing against a cane, then over the winter it is easy for the canker fungi to get in. They like cool conditions best and are very active during the winter and early spring. Although a cane may show leaves, these are only growing on the moisture left over in the canes but once that is used up hen the leaves die. The reason for this is that the canker has already killed the cane over the winter. All infected canes need to be pruned back way below the damage to make sure there are no bacteria left in the cane which could start up again. Pruners need to be dipped in alcohol every time you make a cut as this fungi can infect easily. And as you have already done, must be burned. Once you have done that then a spray with any rose fungicide for black spot will make sure there is nothing left on the canes. Also spray the other roses as a precaution as you don't want to get them infected too.
This canker problem is not unusual and you have probably even encountered it in the tips of rose bush canes in the spring. But when it gets into a canes from the base it makes it harder to see the damage and so it shows up in the spring as dead canes. The light dusting of green pollen may just be that. Evergreen trees are known to shower the stuff in spring. It can also be a residue left over from a spray.