Answer: Very creative idea! My main concerns are that the fine line might cut into tender new growth, and that the fishing line might degrade in the sunlight over time.
I have made a nice trellis with 1" X 2" horizontal slats attached every foot or so between to two upright posts 4-6 feet apart. As the rose fills in, the trellis is well hidden. Also, there some beautiful wood and/or wrought iron trellises available that enhance the look of the rose and add beauty to the winter garden, too.
Remember to train your rose canes as horizontally as possible to the trellis. Horizontal canes will bloom much better along the cane then vertical ones.
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