mingwm10.dll isn't part of GCC as such as you can easily build GCC without it (You can, for example, use Cygwin instead).

A quick google turns up this:

"Dynamic linking with libgcc_s_dw2-1.dll is necessary to throw exceptions between different modules, such as between two DLLs or a DLL and an EXE. Consequently, it is the default for all languages other than C. To disable this dynamic linking, use -static-libgcc. To enable this dynamic linking in C, use -shared-libgcc."