Experts and BHG readers answer.
The pom pom growths that you see are seed heads. It's not necessary to cut them off, because most types don't become weedy from self seeding. And they can be quite ornamental in their own right.
Pruning of clematis depends on which class they belong to. If they bloom early in the season, it's likely that they bloom on old wood, so don't prune in fall or winter except to cut out dead stems. Types that bloom later in the season, bloom on new wood (perhaps on new and old wood). Those types can be trimmed in winter without sacrificing bloom the following summer.