Almost any rose will grow someplace in Arizona. Major rose farms are west of Phoenix and account for at least 60% of all modern roses sold in US commerce. What part of the state are you interested in for growing roses? I've lived in the Phoenix area for over 30 years and grown a variety of modern and antique roses. Some afternoon shade is nice but not absolutely necessary. I also maintain a public garden of 500+ roses that get all-day sun. With a 365-day growing calendar, the low desert is an awesome place for gardening.