Don't remove too much foliage at once, but this spring, start pruning them off one at a time and pluck a few old needles here and there to encourage back-budding. I don't have experience with mugo pines specifically, but in general, pines will thicken at those points where multiple branches radiate out like spokes, and you'll find yourself fighting an inverse taper. Eventually, you'll want to work toward replacing all of the current thick branches with finer ramified branches, but start just by removing some of the wheel spoke branches to preserve your taper. As the tree back-buds and you get more replacement branches, you can continue removing old, thick branches a little at a time.