Yes, inside /mnt/mxe/usr/i686-w64-mingw32.static/include/boost there are many files:
/mnt$ ls /mnt/mxe/usr/i686-w64-mingw32.static/include/
------skipped printout -----
ia64reg.h pshpack4.h xpsrassvc.idl
iaccess.h pshpack8.h ymath.h
iadmext.h pshpck16.h yvals.h
iadmw.h pstore.h zconf.h
iads.h pthread_compat.h zlib.h
icftypes.h pthread.h zmouse.h
honglu@debian:/mnt$
The output that you posted here does not show a "boost" folder in that directory that you did "ls /mnt/mxe/usr/i686-w64-mingw32.static/include/"
You should actually have a directory
/mnt/mxe/usr/i686-w64-mingw32.static/include/boost <<
Went back redid and confirmed, yes, boost folder is there with many files:
/mnt/Eidas$ ls /mnt/mxe/usr/i686-w64-mingw32.static/include/boost
--------skipped, tons of files print out------------
compressed_pair.hpp function_types mpi range.hpp unordered
compute fusion mpi.hpp ratio unordered_map.hpp
compute.hpp generator_iterator.hpp mpl ratio.hpp unordered_set.hpp
concept geometry msm rational.hpp utility
concept_archetype.hpp geometry.hpp multi_array ref.hpp utility.hpp
concept_check get_pointer.hpp multi_array.hpp regex uuid
concept_check.hpp gil multi_index regex_fwd.hpp variant
config graph multi_index_container_fwd.hpp regex.h variant.hpp
config.hpp hana multi_index_container.hpp regex.hpp version.hpp
container hana.hpp multiprecision scoped_array.hpp visit_each.hpp
context heap next_prior.hpp scoped_ptr.hpp vmd
convert icl noncopyable.hpp scope_exit.hpp wave
convert.hpp implicit_cast.hpp nondet_random.hpp serialization wave.hpp
core indirect_reference.hpp none.hpp shared_array.hpp weak_ptr.hpp
coroutine integer none_t.hpp shared_container_iterator.hpp xpressive
coroutine2 integer_fwd.hpp non_type.hpp shared_ptr.hpp
crc.hpp integer.hpp numeric signal.hpp
cregex.hpp integer_traits.hpp operators.hpp signals
cstdfloat.hpp interprocess operators_v1.hpp signals2
honglu@debian:/mnt/Eidas$ ls /mnt/mxe/usr/i686-w64-mingw32.static/include/boost/*.h
/mnt/mxe/usr/i686-w64-mingw32.static/include/boost/predef.h /mnt/mxe/usr/i686-w64-mingw32.static/include/boost/regex.h
boost include folder has tons of "*.hpp" files, and only two regular looking "*.h" files.
Ok so the question is, is your boost installation done correctly, and are you using the correct version of boost ?