plants can surprise you. The areca is a fast grower and will have a complete canopy by this summer. Don't even worry about it. I have small clumps of areca in my front yard (seedling sized plants) and they've seen low 30s regularly during December and even one night at 28 degrees. Of course the outer leaves are burned, but they are quick to recover. I have duranta out in the open in z9b CA and they reguarly see low 30s and mild frosts. There is some leaf damage but thats about it. My best advise is to leave everything as is -- besides raking up debris that has fallen off by itself. When new growth shows up, you will be able to see the full extent of the damage.

So I shouldnt cut the fronds/stems on the areca...will they rot? Or just fall off? My durante have been a problem since last december. They looked awful last winter, they were fairly new in 2006. It took a while but they came back this summer. Now they look terrible AGAIN. I hate the thorns on them. Are they prone to any disease? Right before the freeze, I had sprayed them with a systemic insect killer, thinking maybe something was attacking them. Now I cant tell, not sure if they look better or worse since the freeze:)

Just let them be for now. Dead leaves will be pushed off by new growth, and even if the stems (trunks) rot, arecas are suckering palms and will send out new palms from the roots. If your area is prone to frequent frosts or even light freezes, the areca would not be the best candidate, they will burn every year. I have mine as background foliage, not really expecting them to grow to any significat size, and if they freeze to the ground in a bad year, i can expect small palms to sprout back from the roots.
We must have different Duranta. Mine doesnt have thorns. Mine was labeled "Duranta Repens" aka: golden dew drops. Mine get their foliage damaged almost every year, but i just leave them alone. When new growth appears, i can clearly see the extent of the damage and then prune off the truly dead tips.

Several neighbors have areca palms for years. Last Thursday mornings freezing temps were rare for our area....at least from what I am told last time it happened was 7 years ago. We are less than 4 miles from the Gulf...the way a crow flies. I guess the Gulf usually plays a role in how cold we get. I am not sure how cold we got last week. My husbands car read 33 at 5 AM. My thermometer on the lanai and near the front door only got to 36, but maybe they were too close to the house (about 5 ft away) so they were not accurate temps. My durante didnt have thorns when they were "new" as the plant matured they appeared. I really dislike them. If I didnt pay so much for them, I would probably rip them out but I dont know what to replace them with. They looked great when they were first planted. They circle a sylvester palm on the corner of the home. The lawn guys trim them constantly, they grow like a weed, they have very few leaves except for the outside areas. The thorns are awful. One got me over a month ago, my finger is still slightly swollen from it. Last year I replaced two durantes with plants from home depot. The tag called them cuban gold, duranta erecta. I didnt know they have a thornless variety. I will keep looking.