Mother Nature can frustrate us!
There are over 100 species of the beautiful Coral Tree and the cold tolerance can vary. Many can survive temperatures down into the low to mid 20 degrees F.
Some types can be damaged or die off from slight dips below 30 degrees F.
Even though your tree has lost it's leaves, don't give up yet. Check the branches, do they snap off or bend? If the branches bend, they are still alive.
Scratch the bark, is it green underneath? A live tree should appear green under the outer bark.
Give the tree more time this spring to see if it can leaf out or even grow up from the roots.
When I lose something in my own garden, I try to remember; a loss in the garden makes for new opportunities.
I know it still hurts to lose a treasured specimen, especially a lovely Coral Tree.
These articles have more information.