Azaleas are somewhat of an iffy sort here in Zone 5b, meaning they are supposed to survive our cold winters and bloom beautifully in the spring, but sometimes they do neither. I've lost a couple of them to the cold and while the lone shrub we have now has made it through a couple of tough winters, it didn't always bloom much come spring.
Knowing it is a marginal shrub for me, I've always mulched well, but there are other outside forces that conspire to bring it down from its potential glory. Freezing and thawing, drying cold winds, and scalding winter sun can do a number on trees and shrubs, so a little extra protection may be needed for some of them, including azaleas.
A couple of years ago, I decided to wrap the azalea in burlap. Our local Walmart had plenty of it in their fabric department for $2.49 a yard, so I bought 1½ yards, which was plenty to lay over the shrub and wrap it loosely.
I secured the burlap at the bottom with a hooked bungee cord, so the winds wouldn't blow it away. Other ways of keeping it in place are with ground staples or stakes.