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It tested on Linux Mint 16, and may be be correct for your distr.

Need install mingw32 runtime and compiler

#!c++

$sudo apt-get update
$sudo apt-get install mingw-w64
$mkdir archives
$cd archives 
$tar zxf SDL-devel-1.2.13-mingw32.tar.gz
$sudo cp SDL-1.2.13/include/SDL/*.h /usr/i686-w64-mingw32/include
$sudo cp SDL-1.2.13/lib/*.a /usr/i686-w64-mingw32/lib
$sudo cp SDL_*/*/*.lib /usr/i686-w64-mingw32/lib
$sudo cp SDL_*/*/*.h /usr/i686-w64-mingw32/include
$cd ../
$cmake -DCMAKE_TOOLCHAIN_FILE=xcompile/win32-cross.cmake
$make

If you don't want to use cmake you have to include the folders:

#!c++
source
dep

and link to the libraries:

#!c++
opengl32
pthread
png
smk
bzip2
zlib
aes
lzma