No just leave them alone, I gradually cut the old leaves off, so slowly rid of the ugly look. I think perhaps the spots are from watering them with cold water. if watering in the winter water when the sun is out and only from the bottom, in the morning, and down around the pot rim, keep water off the leaves. That is the lastest advise of this problem. No one has figured it out yet. I think they need winter heat of no less than 60-65 F inorder for them to do well in the winter.

After a number of years of both indooor and outdoor living in the NE my plants have developed dried and split ends. My two very mature plants completely fill thier pots so can I prune the ugly stalks? What should I expect to happen if I do?

I see you just registered today, but where you live is not listed (curious abt the temperature).

Unless you're in some BIG hurry, I'd wait to trim off the ugly leaves until the warmer weather.

Also, if these mature plants really fill their pots, it may be worth repotting them come Spring. How long ago did you last repot them (not for a bigger pot, but for fresh soil)? Should you do so in Spring, then you can also trim off any dry, split &/or damaged roots while you repot & also trim off the ugly leaves then too.