Most of the trees here have a very obvious, long dormant period. Leaves and/or new needles appear mid March, so repotting and similar stuff is late February to March.

Then there are the tropical trees which spend winter indoors and never drop leaves completely. Do baobabs and others have a dormant period? When do I plan on root pruning, etc.? Whenever I want? Does it vary tree to tree?

You repot most tropicals when they are dormant. Although thye do not have a period that they drop their leaves (Although they could if they are not from rainforest environment; Then typically lack of water causes leaf drop). In any case, most tropical trees also have a period during which the are not extending branches.

Baobabs is a dificult one; Being a succulent, I would think you would have to let them dry out till leaf drop. Repot, and keep dry only misting. But absolutely no reason to think this, besides it being a succulent from very in many cases very seasonal ranges