My environment: (WinXP, MinGW (gcc-4.6.2), Cairo-1.12.2, Pixman-0.26.0)

Test program follows:

#include <windows.h>
#include <math.h>
#include <cairo.h>
//#if CAIRO_HAS_XLIB_SURFACE
//    #include <X11/Xlib.h>
//    #include <gtk/gtk.h>
//    #include <gdk/gdk.h>
//#endif
#if CAIRO_HAS_SVG_SURFACE
    #include <cairo-svg.h>
#endif
#if CAIRO_HAS_PDF_SURFACE
    #include <cairo-pdf.h>
#endif
#if CAIRO_HAS_PS_SURFACE
    #include <cairo-ps.h>
#endif
#if CAIRO_HAS_XCB_SURFACE
    #include <cairo-xcb.h>
#endif
#if CAIRO_HAS_XLIB_SURFACE
    #include <cairo-xlib.h>
#endif
#if CAIRO_HAS_WIN32_SURFACE
    #include <cairo-win32.h>
#endif
#if CAIRO_HAS_BEOS_SURFACE
    #include <cairo-beos.h>
#endif
#if CAIRO_HAS_DIRECTFB_SURFACE
    #include <cairo-directfb.h>
#endif
#if CAIRO_HAS_OS2_SURFACE
    #include <cairo-os2.h>
#endif
#if CAIRO_HAS_GLITZ_SURFACE
    #include <cairo-glitz.h>
#endif
#if CAIRO_HAS_QUARTZ_SURFACE
    #include <cairo-quartz.h>
#endif
#if CAIRO_HAS_ATSUI_FONT
    #include <cairo-atsui.h>
#endif
#if CAIRO_HAS_FT_FONT
    #include <cairo-ft.h>
#endif

/*  Declare Windows procedure  */
LRESULT CALLBACK WindowProcedure (HWND, UINT, WPARAM, LPARAM);

/*  Make the class name into a global variable  */
const wchar_t* szClassName = L"CairoTest";

int WINAPI WinMain (HINSTANCE hThisInstance,
                     HINSTANCE hPrevInstance,
                     LPSTR lpszArgument,
                     int nCmdShow)
{
    HWND hwnd;               /* This is the handle for our window */
    MSG messages;            /* Here messages to the application are saved */
    WNDCLASSEX wincl;        /* Data structure for the windowclass */

    /* The Window structure */
    wincl.hInstance = hThisInstance;
    wincl.lpszClassName = szClassName;
    wincl.lpfnWndProc = WindowProcedure;      /* This function is called by windows */
    wincl.style = CS_DBLCLKS;                 /* Catch double-clicks */
    wincl.cbSize = sizeof (WNDCLASSEX);

    /* Use default icon and mouse-pointer */
    wincl.hIcon = LoadIcon (NULL, IDI_APPLICATION);
    wincl.hIconSm = LoadIcon (NULL, IDI_APPLICATION);
    wincl.hCursor = LoadCursor (NULL, IDC_ARROW);
    wincl.lpszMenuName = NULL;                 /* No menu */
    wincl.cbClsExtra = 0;                      /* No extra bytes after the window class */
    wincl.cbWndExtra = 0;                      /* structure or the window instance */
    /* Use Windows's default colour as the background of the window */
    wincl.hbrBackground = (HBRUSH) COLOR_BACKGROUND;

    /* Register the window class, and if it fails quit the program */
    if (!RegisterClassEx (&wincl))
        return 0;

    /* The class is registered, let's create the program*/
    hwnd = CreateWindowEx (
           0,                   /* Extended possibilites for variation */
           szClassName,         /* Classname */
           L"CairoTest",        /* Title Text */
           WS_OVERLAPPEDWINDOW, /* default window */
           CW_USEDEFAULT,       /* Windows decides the position */
           CW_USEDEFAULT,       /* where the window ends up on the screen */
           544,                 /* The programs width */
           375,                 /* and height in pixels */
           HWND_DESKTOP,        /* The window is a child-window to desktop */
           NULL,                /* No menu */
           hThisInstance,       /* Program Instance handler */
           NULL                 /* No Window Creation data */
           );

    /* Make the window visible on the screen */
    ShowWindow (hwnd, nCmdShow);

    /* Run the message loop. It will run until GetMessage() returns 0 */
    while (GetMessage (&messages, NULL, 0, 0))
    {
        /* Translate virtual-key messages into character messages */
        TranslateMessage(&messages);
        /* Send message to WindowProcedure */
        DispatchMessage(&messages);
    }

    /* The program return-value is 0 - The value that PostQuitMessage() gave */
    return messages.wParam;
}




static void
snap_point (cairo_t *cr, double *x, double *y, bool odd_integer_line_width = true)
{
    cairo_user_to_device (cr, x, y);
    if (odd_integer_line_width)
    {
        // round to nearest half integer
        *x = round (*x) + .5;
        *y = round (*y) + .5;
    }
    else
    {
        // round to nearest integer
        *x = round (*x);
        *y = round (*y);
    }
    cairo_device_to_user (cr, x, y);
}

static double
snapx(cairo_t* cr, double ax)
{
    double x = ax;
    double y = 0;
    snap_point(cr, &x, &y);
    return x;
}

static double
snapy(cairo_t* cr, double ay)
{
    double x = 0;
    double y = ay;
    snap_point(cr, &x, &y);
    return y;
}

static void
draw_grid_lines(cairo_t* cr, int maxx, int maxy, int step, double linewidth)
{
    for (int x = 0; x < maxx; x += step)
    {
        cairo_move_to (cr, snapx(cr,x), snapy(cr,0));
        cairo_line_to (cr, snapx(cr,x), snapy(cr,maxy));
        cairo_close_path(cr);
    }

    for (int y = 0; y < maxy; y += step)
    {
        cairo_move_to (cr, snapx(cr,0),    snapy(cr,y));
        cairo_line_to (cr, snapx(cr,maxx), snapy(cr,y));
        cairo_close_path(cr);
    }

  //cairo_set_source_rgb(cr, 0.84, 0.84, 0.84); //paper color: Dim Grey
    cairo_set_source_rgb(cr, 0.64, 0.64, 0.64); //?
    cairo_save(cr);
    {
        cairo_identity_matrix (cr);
        cairo_set_line_width (cr, linewidth);
        cairo_stroke (cr);
    }
    cairo_restore(cr);
}


static void
draw_grid(cairo_t* cr, int pw, int ph, int zoom)
{
    cairo_save(cr);
    {
        // line positions in mm
        if (0 < zoom && zoom <= 100)
        {
            draw_grid_lines(cr, pw, ph, 1000, .2);
        }
        else if (100 < zoom && zoom <= 250)
        {
            draw_grid_lines(cr, pw, ph, 1000, .2);
        }
        else if (250 < zoom)
        {
            draw_grid_lines(cr, pw, ph,  500, .2);
            draw_grid_lines(cr, pw, ph, 1000, .4);
        }
    }
    cairo_restore(cr);
}

static void
draw_paper(cairo_t* cr, double sf, int pw, int ph)
{
    double shadow = 3.0 / sf;

    cairo_save(cr);
    {
        cairo_rectangle (cr, shadow, shadow, pw, ph);
        cairo_set_source_rgb(cr, 0.0, 0.0, 0.0);
        cairo_fill(cr);
        cairo_rectangle (cr, 0, 0, pw, ph);
        cairo_set_source_rgb(cr, 0.84, 0.84, 0.84); //Dim Grey
        cairo_fill(cr);

    }
    cairo_restore(cr);
}


PAINTSTRUCT  ps;
HDC          hdc;

void dopainting(HDC hdc)
{
    cairo_t *cr = cairo_create(cairo_win32_surface_create( hdc ));
    // dark gray background
    cairo_set_source_rgb(cr, 0.5, 0.5, 0.5);
    cairo_paint(cr);

        draw_paper(cr, 1.0, 500, 500);
        draw_grid(cr, 500, 500, 100);

    cairo_destroy(cr);
}

/*  This function is called by the Windows function DispatchMessage()  */

LRESULT CALLBACK WindowProcedure (HWND hwnd, UINT message, WPARAM wParam, LPARAM lParam)
{
    switch (message)                  /* handle the messages */
    {
        case WM_DESTROY:
            PostQuitMessage (0);       /* send a WM_QUIT to the message queue */
            break;
        case WM_PAINT:
            hdc = BeginPaint(hwnd, &ps);
            dopainting(hdc);
            EndPaint(hwnd, &ps);
            ValidateRect(hwnd, NULL);
            break;
        default:                      /* for messages that we don't deal with */
            return DefWindowProc (hwnd, message, wParam, lParam);
    }

    return 0;
}