I have a very sick Ponytail Palm. It survived the freeze here in Houston and just when I thought it was ok to uncover it, it got cold (not freezing). Today I noticed the ferns were falling out. When I checked on it, the ferns just fell out at my touch and the trunk was wet and mushy. So I cut it back to past the mushy part of the stalk. Is there anyway I can save it?
Ooh, boy, do I hate to say this, but...I think your palm is a goner. That 'wet and mushy' description does not sound good. But, anyway---welcome to the Forum!
Not being a true palm, they can regenerate new shoots from a lopped-off trunk, so it is possible, but cold & wet will just cause more mush.
Cut back until you are below any browned-off wood. Important: disinfect the cutters after each cut (use rubbing alcohol), so that you don't spread the disease from the top to lower down (yes, it's tedious, but it does make success in saving the plant much more likely).