I went there for a week for work, and the only running I did was indeed in the gym. I did not notice a single recreational runner, but then I was mainly in the city or on main roads / business parks out of the city. The park areas I saw were more tourist attractions and I get the impression (perhaps unfounded) that running in such tourist locations might raise a few eyebrows.
I would not dare try road/street running in Beijing though - pedestrian traffic is too dense and crossing road traffic felt risky enough even at a green light with the full awareness of walking pace.
As for the weather, the year I went it was hot and humid in September/October, and freezing cold and snowing in December.
Agree with Joolska that you might be ok further outside of the city - but you'd need some good local knowledge...