I just clipped my mare for the first time this last week so I don't have a huge list of pros+cons yet but I can tell you what I've heard/already noticed.
A MAJOR pro for me has been that she sweats SO much less when I work her. For instance, with all her winter hair, she'd be soaking wet after a ride. It would take forever for me to get her cooled down and dried off, but now that she's clipped, she only sweats under the girth and the saddle so cooling her off is a quick thing.
Another pro is that she looks pretty darn cute with her clip.
A con, I guess, is that you have to blanket (and super stay on top of possible weather changes) and you can't let your horse go blanket-less on a sunny, cold afternoon, or something, because they might get too cold. That doesn't bother me since I'm not inclined to do that. But others might.
For me, the pros definitely outweigh the possible cons.
And here's a picture, just for funnsies. I didn't do a full trace clip because she's not worked really hard and I really wanted to just clip the areas she sweats most. I might do a more full trace later if it looks like it might be necessary, but so far, a modified trace seems just fine.