hardy cactus in zone 7

[Phisherman]

I'm in east TN and have a rather large cactus collection (about 100 specimens). I have a place that gets full (brutal) sun and would like to plant a cactus that survives East Tennessee winters. I have an American cactus (from the USA west coast) which I propagated and tried to toughen it up, but I think it may have died due to frost. I see large cactus growing in various places (Knoxville, Oliver Springs, Oak Ridge, etc) that have been growing for years and they produce summer bloom. Can anyone tell me what cactus will grow outdoors in my location?

[Phisherman]

Got this yesterday, locally outdoors. Currently in my truck bed, in a garage near a row of windows. I think I might cut it into 3 parts, each with a node. Although the mother plant is hardy, I need to keep these from freezing until I can figure out what to do next.

I'd appreciate anyone to identify this cactus cutting.

I rooted a pad cactus (different kind) last summer in a gravel-filled clay pot, outdoors morning-to-noon full sun, with just enough water to wet the clay saucer. Conditions must have been ideal; it grew roots in a week.