Before I address this, I have to ask. What is "emo" to you? The way I originally heard the term used in a non-musical context, it was to derisively describe who were unnecessarily whiny or complaining about things while still having it good for the most part.
Cloud's personality barely changed between the time they left Midgar and when Aerith got killed. And even after that, he's just more driven to beat Sephiroth. At no point before they get to the Northern Crater and he goes missing does he fit that whiny complaining archetype I'm thinking of.
As for Mideel, are you talking about the flashback in the Lifestream? I'm not seeing it. Before he left to try to join SOLDIER, Cloud bragged about how he was going to be the next Sephiroth. And then failed to even get accepted. Considering how we see in the same series of flashbacks how he desperately wanted to prove himself to others, is it really surprising that he might decide not to show his face because he didn't match up to his boasts? At no point did he complain about not making it in SOLDIER. He was just pretty matter of fact about it and about why he hid his face. If I agreed that he was being emo at that point, I'd have to accept that anytime someone felt shame or disappointment for not reaching a goal, they're being "emo." To me that's a huge reach, at best.
For most of the game, Cloud was pretty upbeat. In fact, one of the common complaints about his personality in Advent Children was that it seemed like such a major departure from how he was in FF 7
As for Squall not being emo, going off how I've always understood the term, he doesn't fit either. Cold, yes. Aloof, definitely. Dismissive and distant, certainly. a$$hole, you can make a good argument for, at least for much of the game. Emo though? Again, I don't see it.