It should be warm enough for you to cut out all the rotted,smelly and shriveling parts to solid wood. I dont know how far the rot is going-but if it hasnt reached the base,its going to live. At worst,the trunks might die-but that big caudex has a strong root system after all these years and new stems will grow like rockets.

I also think you should get rid of all the rot. Usually when ponytail palms get tip damage, they branch out. It might actually end up looking fuller if it does live, maybe mother nature gave your plant a good pruning. A 13 year old ponytail palm should be pretty established and hard to kill.

Good luck!

Thanks for responding, I really appreciate it. Somehow I missed your follow ups,& re-posted a minute ago, so ignore. Thanks again so much! Just for fun I'll re-post alil follow up of my own,just to let you know all is well w/it-(fingers crossed)-Pat

My 13 ft ponytail (15years) is on Town Lake and really got the North wind freeze also so keep me posted on yours. All of the fronds have turned white, hard, and most have fallen off last week. I clipped short the really white ones but have not clipped all the way to the top - hard to reach. The smooth bark seeped and then split and chunks appear to have separated from the inside of the two trunks. Should I clip the top fronds back to a couple inches also - or are we to look for something new from the ball?