The breakage of new fronds that you described has also been observed on some other kinds of palms that were cold damaged this winter. It is too soon to tell what the ultimate outcome will be for your palm, but the fact that it is continuing to produce new fronds is a good sign.
It is best to allow partially brown fronds to remain on the palms, since the green areas in them will continue to manufacture food for the palms. Even when the spear leaf (the newest, unopened, spear-like frond) pulls out it does not automatically mean that the bud of the palm is dead. There is a chance that new growth may emerge from the top of this trunk.
In the case of the areca palms, even if some of the trunks have actually been killed by the cold there likely will eventually be new suckers arising from base of the palm. In time these suckers will grow large enough to replace the dead trunks.
For additional information on the kinds of cold damage symptoms on palms that have been observed this year, see the attached fact sheet.
The article has been updated successfully.