Actually, I think Tenzin is quite expressive. It's just that he tries very hard not to since, well for me at least, he thinks that being an air nomad, he has to be calm and peaceful all the time. But it's obvious he has a hard time keeping it all in, especially when Korra gets into the picture. I mean, he's exploded in anger several times already, and was quite bashful when Korra called him out on the whole Lin-was-my-ex.
I love how we see bursts of enthusiasm from him; he's a great mix of Aang's "try to please everyone, be responsible" side and Katara's "go all out for what you believe in" side And I love how he roots for Korra during her matches!