Growing up we had shih tzus. If you keep their coat trimmed they are as active if not more active in the summer than most breeds. There is a trainer around here (quite an aversive one strangely) that does quite well in obed with them. There are also a few doing agility.
I just figured with the squished face summer could be rough. Most of my Shih Tzu experience is from my uncle's dog but she's not exactly well bred and she's pudgy. She also has a collapsing trachea. I took her for a 20 minute walk around the block on a hot day over the summer and started to get worried she was going to heat stroke, she barely made it around the block. But she's probably a bad example of the breed. She is awesome at obedience though, a breeze to train, really smart. But really boring.