A. Growing anything under a walnut is a problem, as the tree emits a growth inhibitor called juglone. Another problem would be the dry condition, due to root competition and shade. None of these are conducive to growing a rose. My best suggestion is to try a large pot with a rose planted inside. Any rose from miniature to any of the teas, etc., are suitable. In the fall, remove the rose or roses and bury in the vegetable garden, so they are protected from winter frost.
Master Gardeners of Ontario