Lantana: The native Texas Lantana (Lantana urticoides) is hardy to zone 8 and should come back from the roots without any problems. Some of the non-native and hybrid varieties of lantana that are more tropical may not come back.  It is recommended to cut lantana back to about 6 inches from the ground in mid-late winter.  The concern with cutting it back in the fall is that wet, mildly cool conditions can leave the plant vulnerable to disease.

Esperanza: This plant should be cut to the ground. There are, however, differing schools of thought on when.  Some cut it back to the ground after the first frost, others wait until late winter to prune out the dead limbs. The argument for waiting is that when you prune, you are creating entry points for disease. So if you were to prune to the ground and cover with mulch you would be setting your plant up for failure (rot, disease, etc). If it looks unsightly to you, you could prune it to a foot or so above the level of the mulch.  Esperanza is not fully cold-hardy in your zone, but it’s pretty close. If you were to have a really cold winter (15-10 degrees Fahrenheit) then it may not come back from the roots. 

Mulching is great! I highly recommend doing this! Mulching helps to keep the roots warm because the air-pockets in the mulch act as an insulator (like a feather-down jacket) and the microbes in the first 6 inches of the soil give off heat as they work to break down organic matter (that the mulch also helps to contribute). A great source of organic matter for hungry soil microbes is a layer of leaves under the mulch.