Not sure to report this as a bug or a feature request. According to this post:
http://aurora2.pentarch.org/index.php?topic=8495.msg104912#msg104912, "Ground units of species with certain types of home world may gain capabilities for free". I have not done the testing to see if this is implemented behind the scenes, but in a recently created game with a player race that has a home world of the desert mountain type, when creating ground units I still need to research and pay to apply the desert and mountain capability on ground forces.
If it is implemented behind the scenes, then it can be easy enough to remember if you only have one race, but it becomes more complicated if you conquer and integrate a different race with, say, a jungle home world and start building ground forces with them to mix into the main army.
If this is already implemented, I would like to suggest an interface update to reflect if a particular ground unit already has a terrain specialty, and if it is not, then perhaps a check could be made to award the relevant techs for free and allow free updates with the relevant terrain specialties.