Rooting of dormant Azaleas in winter can be successful.
Here's a link that explains one proceedure. Be sure to read the last sentence yhat applies to deciduous Azaleas.

Don't overlook the Azalea's roots that are still in the ground. They will probably produce new growth in the spring.
Trim the remaining stem at a 45° angle with a sharp knife or pruners, Cover the cut edge with plastic baggie and secure with a twist-tie or rubber band. Remove when signs of new growth appeat in the spring.
Good luck!
Rb

Razorback's link didn't come through. Here are some links for rooting deciduous azaleas:

http://www.tjhsst.edu/~dhyatt/dormant.html

http://www.azaleas.org/azpropagate.html#cut

Sorry about that!
Had trouble with GW all day Friday and for a time, couldn't load any pages.
Here's the link, by Don Hyatt, probably same as one of the above, but includes drawings of each step.
Rb

Here is a link that might be useful: Rooting Azalea & Lepidote Rhododendron Cuttings

I trimmed cuttings and planted in sterile medium, eventually under 14 hour lights. No idea if the cuttings have struck, but they seem to have broken dormancy and are breaking bud. Should I be thrilled or terrified?

Neither yet - just patient. Breaking buds doesn't necessarily indicate rooting so it's a little early to dance :)