The best time for me is now actually for propagation. They're a woody stem so it's a Lil tougher and I just got lucky. I know they really start growing buds and new stems in the winter-super early spring.
I started with just little 2 to 3 inch cuttings from the tops, sides, wherever using root tip gel. I also extracted extra juice from a willow branch so it was an even higher concentrate for root tip growth. I cut about 20 of each one and just sat it in a pot outside and covered with leaves.
Some died but most survived. I honestly neglected them and just happen to remember I left the pot in the woods in the summer and WAH Lah! I did this seriously 3 years ago and won't do it again because it took so long. You may be able to cut different or bigger sizes too. If you cut an azalea now tho your gonna risk blooms for the spring.
I'm sure theres YouTube for this like other prop. vids. I just feel I got lucky. Other plants I've tried that I thought would be easier died almost in days.
this is actually another type. One of those big wispy ones, but nice huge flowers in the spring. But notice the green, nows the time for me to cut again..here in NC at least.