Answer: There's a couple of factors to consider. Ogden is zone 6 and Tucson is zone 9. Tucson will get some freezing temperatures, but not with as much regularity or severity as you will. Some opuntia (those with the pads) cactus are native to colder regions and are hardy. For example, northern Arizona with an elevation of 6600 feet has small prickly pears that survive on the open range. But there are so many varieties that I have no way of knowing what you have or if it's native to the Sonoran desert or a colder region.
On the other hand, your roses sound as if they do okay, but they might be bred to be hardy. So many variables! To be on the safe side, I'd bring the cactus in and put them in as sunny a location as you can. Don't overwater--once a month should be enough. If you have lots, you might want to try one to see how it does outside. But when we have frost warnings in the desert, we encourage people to protect their cactus because the tips (growing points) can freeze. I hope this info helps!
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