As many garden tasks as I have, I do not have time for pinching them back. Towards the end of June or first of July, I cut them back to about six inches. They look a bit sad for awhile and other garden plants are useful in camouflaging that, but soon they grow out of it. By the time they are intended to bloom, you would never know they had been so "abused" just a few months earlier.
Mums are one of the easiest plants to propagate, too. If you want more plants, when you cut them back, simply stick the cuttings in soil and keep them watered. Soon you will have a whole crop of them. I learned this by accident a few years ago when I was potting some up and tossed the scraps aside. Even in poor soil and a fair amount of shade, they quickly began to grow!
Some have the problem of mums dying over the winter. Typically the problem is that mums planted in the fall do not have a chance to get established before winter. Ideally mums should be planted much earlier in the season, but usually they are more available in the fall. Marketers know that pots full of blooming flowers so late in the year are irresistible to someone looking for quick fall decorations. If they are planted this late, mulching may help. They are also more apt to survive the winter if not cut back until spring.
I have rescued mums and successfully overwintered them in the garage or a sheltered area until I could plant them in the spring. I do water them if they are not getting rain and snow for moisture. I recently noticed that though I have only bought a couple of mums in my life, I have gathered quite a collection of them this way. One benefit of various mums is an extended bloom time, as they bloom at different times.
Insects of all sorts are attracted to mums. Jim said amber is especially attractive to bees and wasps and that they would swarm around the lights on the utility vehicles he worked on. That seems to be the case with mums, too. There have been a lot of honey bees visiting this one for sure. They are always a welcome sight since pesticides and disease have killed so many of them.
For those who like something a little more exotic, there are mums for you, too. The last two mums pictured are a spider mum (I believe the cultivar is 'Lava') and a quill mum that I got at the end of a mum show at the botanical garden I used to work at. Though not all show mums are winter hardy, these have survived for several years in my garden.