Another tidbit is the fact that in order to get upgrades for a unit, the retraining facility does not necessarily need to be able to create the unit being upgraded. For example, if you have a province with Legendary Armory, but no Horse Dojo, you can still move a cav unit into it, retrain them, and they will pop out with a lovely little gold shield. However, if they have taken any losses, those losses will not be replaced if the required building is not present.

I believe you have to have at least one unit training building in the province however... never tried it, but I know when you click Train in a province w/o any training buildings, it won't let you open the window. So you'd at least need a spear/archer dojo or something.