If you have your squad set to train or whatever with fewer than the maximum number of dwarves, they'll cycle on and off duty periodically. This is good, because it gives them time to do things that give them happy thoughts and avoids the "enraged/depressed by long patrol duty" unhappy thought. Also and independent of this, at the start of every month your military will go off-duty for a blip while their orders for that month are handed out.
I think the consequences of this are twofold. Whenever a civilian dwarf without significant military skills goes on duty, he gets an "unhappy about the draft" thought. And whenever a military dwarf without significant civilian skills goes off duty, he gets an "unhappy to be relieved from duty" thought.
So the worst-case scenario is to have a militia full of dwarves who have no military skills — recruits — who also have no civilian skills — peasants. They'll just hate their lives.
The good news is the problem solves itself eventually. Dwarves who make it through boot camp without going Private Pyle lose the "unhappy about the draft" thought because they gain military skills, and eventually they become legendary fighters and stop going off-duty at all.
In the meantime, a good tactic if you need to minimize unhappy thoughts is to draft only skilled-but-useless migrants, like that high-master beekeeper who's been camped out in your statue garden since the spring. He'll be unhappy about going on duty until he skills up to pretty minimal levels, but he won't be unhappy about going off duty.