I don't if Smalltalk can handle multiple files, but you can use the Window API, show WIN32 Help API for message WM_DROPFILES and the API function for you is probably "DragQueryFile" look there. This function gives informations how many file are dragged and this function returns the file name for specified dragged number of file. So you can iterate over all numbers and then require the file name for the actual number.
Perhaps this link http://www.codingcrew.de/programmierung/win32hlp.php
I hope this can help you.
Here the discription for WM_DROPFILES the origin for drag and drop of files
The WM_DROPFILES message is sent when the user releases the left mouse button while the cursor is in the window of an application that has registered itself as a recipient of dropped files.
hDrop = (HANDLE) wParam; // handle of internal drop structure
Value of wParam. Identifies an internal structure describing the dropped files. This handle is used by the DragFinish, DragQueryFile, and DragQueryPoint functions to retrieve information about the dropped files.
An application should return zero if it processes this message.
DragAcceptFiles, DragFinish, DragQueryFile, DragQueryPoint