Depending on the size of the file, you could use a login script, but I would recommend setting up a batch file.
If you use xcopy, you can specify which file you want to copy, and where you want to copy it to really easily. just go to a command prompt, and type xcopy /? for the description of the switches that are available with the command.
your best bet is to create a shared folder on the destination machines that is hidden: use a dollar sign at the end of the sharename. Then, you can set a script to run that looks like this: xcopy d:\databasefolder\filename.txt \\destinationmachine\sharename$\ and the file you specified will be copied to the destinationmachine\sharename$ directory....and since you want to copy it to multiple computers, just add another command line to the batch file for each computer with the appropriate path and sharename so the batch file will copy it to all computers.
Finally, go to Start, Programs, Accessories, System Tools, Schedule tasks, and specify the script you want to run, and when.
Hope this helps.
Mike