What am I missing?

Well ... it's not finding the gsl headers.
The only way I can get it to build on Windows is to set CPATH to the directory that contains gsl/gsl_nan.h (*not* the directory that contains gsl_nan.h), and set LIBRARY_PATH to the directory that contains the gsl libraries.

That CPATH setting will do the trick for you, too, but for the LIBRARY_PATH setting to work, you might (not sure) also need to modify perl/lib/ExtUtils/Liblist/Kid.pm. If you look in that file, you'll find the following code:

    if ($VC and exists $ENV{LIB} and $ENV{LIB}) {
        push @libpath, split /;/, $ENV{LIB};
    }
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Immediately below that insert:

    if ($GC and exists $ENV{LIBRARY_PATH} and $ENV{LIBRARY_PATH}) {
        push @libpath, split /;/, $ENV{LIBRARY_PATH};
    }
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Alternatively, you could probably just alter the libpth setting in lib/Config_heavy.pl to include the directory that contains the gsl library files.

It should then build for you - though I'm a little concerned about the structure of your gsl library. You say that gsl_nan.h and friends is in GSL_DIR/gsl, but that GSL_DIR points to %SHORTPATH%\PKGCON~1\bin\PkgConfig. I can't follow that, and even if I could it wouldn't sound right to me.

Be prepared for a number of test failures when running the Math-GSL-0.22 test suite. Despite the failures, you can of course install it anyway - you may find it works quite well for you.

Cheers,
Rob

UPDATEs: Btw, if you want to build a Math::GSL that passes all of its tests, I'm pretty sure version 0.14 fits that bill - there may, of course, also be later versions that pass all tests. I think those earlier versions are missing some of the functionality of the later versions, and it's this added "functionality" (along with a few test suite bugs perhaps) that's currently breaking Math::GSL on Windows.

0.22 actually builds better than I remembered - so long as you're building against a dynamic (dll) build of the gsl library. You'll get segfaults if you build against a static library, owing to the way in which the Math::GSL error handling is structured. Here's my 'perl build test' report for 0.22:

Test Summary Report
-------------------
t\CDF.t          (Wstat: 512 Tests: 794 Failed: 2)
  Failed tests:  481, 523
  Non-zero exit status: 2
t\Matrix.t       (Wstat: 0 Tests: 238 Failed: 0)
  TODO passed:   209-212
t\Vector.t       (Wstat: 0 Tests: 142 Failed: 0)
  TODO passed:   141-142
Files=52, Tests=3636, 39 wallclock secs ( 2.03 usr +  0.31 sys =  2.34
+ CPU)
Result: FAIL
Failed 1/52 test programs. 2/3636 subtests failed.
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As you can see, nothing to worry about except for tests 481 and 523 in t/CDF.t

I've only just now worked out that the reason I had to use CPATH and LIBRARY_PATH was that my lib/pkgconfig/gsl.pc was written to specify pathnames in msys-style. If paths are specified in that file using normal windows-style pathnames then there's no need to make use of CPATH and LIBRARY_PATH.
(My gsl library was built in the msys shell - hence the use of msys-style paths in gsl.pc.)