Signs of a good temperament in a foal, IMO, are that it's bold and cheeky and has to INVESTIGATE that scary thing over there because it might just be edible/fun to play with.
Signs of a good temperament in a stallion I'm not so familiar with but again IMO a stallion should be bold and a little bit cheeky, but kind and well-mannered (manners are a training thing more often than not, but you can't tell, with a horse that's not yours, whether his arrogance is trained or not). I'd be quicker to choose a stallion that I knew was ridden regularly by a teenager or young adult with no issues over a stallion that was unproven or unreliable undersaddle. You want to look at his other progeny, how they are on the ground, how they are undersaddle if his oldest are old enough.
You also want to look at the mare. Is she a bolder type or is she more timid?
I personally LOVE bold and cheeky. It's not ideal for some people but I like a horse that isn't afraid to push the boundaries a little. I'm a very dominating type of person so that really suits me. Bold horses are generally steadier and have fewer fears than a more timid, nervy type, and they're generally more confident jumpers (which is what I do) - but then again, if you get a sensitive type over their fears, they make wonderful, clean, careful jumpers, because they generally hate knocking poles. But they take a LOT more skill and experience to train, and a heck of a lot more patience, because if you over-face them ONCE, they may never want to jump again, depending on the horse.
You're talking Morgans so you could be talking about any discipline. I know someone who has a Morgan that she does dressage with and will eventually event on when he stops leaping over a 6" cross like it's 6' but I also know that they are used for Western disciplines and I'm pretty sure I've seen photos of them being used for saddleseat as well. I believe they are a very versatile breed. In fact I'd have them except for their reputation (locally) of being rather TB-like in their temperaments. And the fact that here, they're hard to come by, and generally very expensive.