I see two things here:
1.) The other commenters don't mention that "chestnuts in the fire" points to a dangerous situation. If you pull someone's chestnuts out of the fire, you are saving them from a dangerous situation. For example "The Prime Minister's advisors pulled his chestnuts out of the fire after the budget disaster."
2.) The fact that nobody else has mentioned this figurative meaning should answer your question "Do English speakers use them a lot". They really don't.