We are having our bathroom re-done. We tried to get it done in warmer weather but it just didn't happen (long story). Anyway, we only have one bathroom so we are using our trailer. So far the temperature has been fairly mild but the next couple of days it'll be dropping. It will be dipping below freezing at night (lower 30's to mid 20's)but rising up above freezing during the day. This may go on for 3 or 4 days.
How great of a danger is there of the pipes freezing and cracking?
If i understand you correctly the styrofoam is the insulation. If you know someone who has a metal electrical fish tape you can use that to cut through the styrofoam. Just cut the loop off the end to make it sharp. As long as you don't have go through studs that should work. If you can't find one try using a wire hanger. Unbend it and make it as straight as possible. If it's tough feeding it throught the wall you can try twisting it to act as a kind of drill bit. That may make it go easier.