Frozen Pipe(s) — How to Respond?
The bursting is actually caused by the ice. Ice takes up more room than the amount of water it was made from, ultimately bursting through copper. 

If you had a trickle of water, you may have been better off leaving the taps all open in hopes of keeping the water flowing. Flowing water (even a trickle) is less likely to freeze than standing water. One of the ways to prevent frozen pipes is to leave the taps open to a trickle (obviously not a good long-term solution, but can work in a pinch in locations with rare temp drops). The open taps also allow for lateral expansion of the water that may freeze. 

At this point, if the pipes are frozen solid, and are behind walls so that you can't get to them, you pretty much have to wait it out and hope they haven't burst. If they have, depending on how many places they burst, you may be able to go in and fix a few patches. But if there's more than a few splits, you may end up wanting to pull the whole thing out and replacing it all (and this time ensuring everything is properly insulated). 

Good luck!