I grew up with a rose garden (That was all I got), so I've been trimming them since I was in 7th grade. If you include close ups of the vinework of your latanas, like angle your camera from under the blossoms if there are any, then I could give you specific guidance. The time of year might not be as important as the placement, severity, and style of cut. You probably already know to cut just above the nip, and to angle your cut top down, to minimize rain getting in the wound (not sure if it rains much where you are). And the dead head to increase blooms. It is fine to just prune the few inches under a dead head which are inches that are going to turn brown and fall off anyhow. In general, I wouldn't prune very much at any one time, regardless off time of year, because I like tall rose bushes. If you like short bushes, then yes you can cut them way down, but remember to cut above each nip, angle the blade down and inward so the wound kind has an overhang to keep rain out, and I would stagger the height of each major cut by many inches so your blossoms show more instead of all being at one height.