I think you could get away with 3v on the mini, on the 3.3v pin.but I wanted to use a netduino mini since I have a fair understanding of C# and I'm pretty sure that doesn't run on 3V
Also, this site I think has a lot of "in car" stuff, like this:
http://www.mini-box....8&category=1264
...which you might think about using with a small lead-acid battery. Just throwing stuff out there.
Good luck with this!