Is it safe to leave my carbon bike in my stationary trainer for extended periods of time? This time of year, I leave my race (carbon) bike on the trainer and when nice enough, just ride my rain/wet/commuter/cx bike.

I do replace the 'race' skewer with a steel skewer for trainer use.

Will it damage the carbon if I leave the bicycle clamped and ready to train on the trainer? Should I release the clamp every time I'm done training?
If this is the kind you have, then leaving the bike in there should make no difference whatsoever. This trainer clamps onto the rear axle, it doesn't even touch the frame. When you're off the bike, the frame doesn't have to do anything except support its own weight - there's no possible way it could get damaged. 

You're probably less likely to damage the bike, since you won't be knocking it over.