First, lets try to understand the difference between mosquito mating, and mosquito breeding. Mosquito breeding is dependent upon standing water where the female can lay her eggs that hatch into larvae and is an important part of the life cycle. Mating can occur about anywhere, and is not restricted to any particular type of plant. So dead decaying horse herb leaves would not constitute a mosquito breeding habitat.
Horseherb Calyptocarpus vialis (Straggler daisy) is semi-evergreen, remaining green and blooming year-round in temperate climates. It can go dormant in cold winters. It ordinarily blooms yellow March to November, has low water use, and can do well in sun, part shade or shade. It is a fast growing plant and is considered invasive by some, and has both its detractors and admirers. I’m going to provide you with two links that will give you information about this interesting plant.