I mainly play clarinet and sax, but I'd like to pick up a bit of trumpet to be able to play all the big band instruments (albeit quite badly for some of them). However, I've heard that playing brass instruments can damage your woodwind embouchure, which I really don't want.
I'm not sure how true this is, as I know someone who doubles sax and trumpet, and someone who doubles clarinet and trombone, and they seem to manage. I've also dabbled in trombone myself, and that's not seemed to affect embouchure for other instruments, but I think that trumpet might since the few times I've played one the smaller mouthpiece made it more stressful on my lips (although that could have been poor technique).