This has been the hardest winter since 1976 when the Chesapeake Bay froze!  First we had a very unusual early winter with the temperatures swinging from 60 or 70 degrees F to 10 or 20 degrees F, stressing the plants severely.    Then in the later part of the winter the temperatures went down to -2 degrees with a strong wind which did two things to plants.  First, the plants had to deal with the unusually low temperatures and frozen ground and second, as the soil was frozen it could not replace the water the wind pulled out of the leaves of evergreen plants, stressing them even more.   This is classic winter burn for evergreen plants.  Even though the  the Windmill palm is the most cold hardy, it is not equipped to deal with the winter we just had!  Some of the information I found was that it is hardy to 10 degrees F or grows best in USDA zone 8-11.  In Ocean Pines you have the Assawoman Bay and the canals helping keep the temperatures from fluctuation severely, but this cold winter has been cold everywhere!   My suggestion is to wait till the temperatures warm up in March and then trim off the dead foliage and the tattered ends.    I don’t see how hydrogen peroxide would help the tree in any way, your palm doesn’t have a disease, just cold damage.