More than likely, the dry conditions of winter (causing
wood to contract) is what is causing the elements of your
door to separate. Wood glue may help, but in the changing
seasons, it's apt to separate again. Wood filler is good,
but unfortunately, you'd have to sand again to bare wood
for it to fill & dry properly. Something with elasticity
(like silicone caulk or adhesive) would allow the door to
expand & contract with the weather/changing seasons. Small
cracks can always be filled with a fresh coat of paint.
It's still a good idea to sand around the joints separating
the mullions from the panels if you're adding any adhesive or
filler. I hope this helps.