Well, the normal C++ compiler you use for Windows is going to be Visual Studio, whereas Fedora uses gcc. (For C++, the compiler is g++).
Often there are differences. I got burned big time in high school when I couldn't figure out how to get the code that worked perfectly fine on my home copy of Visual Studio to work on my school's CodeWarrior. (I imagine that it's just that the build system was configured differently, but of course, I didn't know WTF to do and my final project wouldn't compile...yeah, not fun.)
So it's better to use whatever your school is using. Fortunately, if they're using Linux on their computers, there's probably a free Windows version of the stuff they have.
As for setting up a proper development environment in Windows, I don't really know how your school is doing everything, so I can't give you specific answers. Cygwin will help you set up a Unix-like environment on Windows. And then you'd go about setting everything up...I don't know whether there's a package management system in Cygwin or whether you have to compile all the stuff you need from source. (Which would be a pain.)
The easiest way to do it, as far as I'm concerned, would be to set up a Linux partition on your home computer. You can get Fedora for free, obviously, and Ubuntu is pretty popular for home users. Then use Synaptic (in Ubuntu, or apt-get on the command line if you already know what you want) to get all the software that your school is using.