There is no right or wrong general answer to this question. Some people prefer the tidy appearance of a cleaned-up bed, others prefer to let nature take its' course until spring. Some years I do nothing, some years I trim the ugly stuff above the ground. Seed pods/heads should either be discarded or saved. Letting them fall in abundance at the base of the mama plant is usually regrettable. I think the most important thing is putting on a good layer of fallen leaves, which I try to do whether I've trimmed anything or not. I wouldn't cut down anything still green like your pictured plant.
I've not tried the bucket, but have had good results with putting a pile of leaves on questionably hardy stuff, like Bougainvillea, Persian shield (Strobilanthes dyerianus,) Caladiums. Failures in overwintering can usually be linked to excess moisture combined with cold, not necessarily just cold. The leaves aid in that regard, directing water away somewhat, improving drainage, and helping to moderate the soil temp from wild fluctuations. Luckily we don't have to worry about frozen soil.
Regarding trimming Lantana, numerous people have told me to not trim them until spring because fall pruning can sometimes kill them.
Hibiscus macrophylla blooms on old wood, so trimming anything now besides obviously dead parts could cause you to miss next years' show. When these start showing green buds in the spring, I trim lightly for shape, and to make sure none of the branches are too long/floppy to stay upright, then prune more heavily as necessary after the blooms are finished.
Generally, even when things are trimmed neatly in the fall, it's usually necessary to do some of it again in the spring to address tips/branches that might have died over winter, might have grown more than you thought it would, you notice that the really vigorous buds are much lower on the stems...
