No – don’t cut it to the ground now. Despite the powdery mildew, the plant is still creating and storing a lot of energy right now, and cutting that short by removing most of the plant will not give it the benefit of the full season. However, next late winter/early spring, go for it! You can cut it back quite hard (honeysuckle is nearly indestructible once established), or wait until you start to see the new growth beginning to emerge and then cut out anything dead and just cut the live parts back.  The trick about treating powdery mildew is that most commercially available treatments are preventative, not curative. In other words, once the disease is established, they won’t get rid of it. Powdery mildew infections actually take place in spring – it’s that in summer, the fungal spores have developed enough to become visible in the form of that powdery substance on the leaves. So treating powdery means starting in spring, when the foliage begins to emerge. At that point, it hasn’t yet developed a protective, waxy cuticle so is very susceptible to infection. To reduce the chances of powdery mildew recurring, there are a few steps you can take. One, when the leaves drop, remove all the fallen foliage. The spores overwinter on those leaves and can readily re-infect the plant in spring when conditions are ideal. Additional measures you can take are to make sure the plant gets the appropriate amount of sun and good air circulation (this helps foliage dry more quickly), and to avoid wetting the leaves when you water. If you have a sprinkler system, consider adjust the head so it does not spray the plant itself with water.