You have two options:
Install cron as a windows service, using cygrunsrv:
cygrunsrv -I cron -p /usr/sbin/cron -a -n
net start cron
Note, in (very) old versions of cron you need to use -D instead of -n
The 'non .exe' files are probably bash scripts, so you can run them via the windows scheduler by invoking bash to run the script, e.g.:
C:\cygwin\bin\bash.exe -l -c "./full-path/to/script.sh"
Just wanted to add that the options to cron seem to have changed. Need to pass -n rather than -D.
cygrunsrv -I cron -p /usr/sbin/cron -a -n
I figured out how to get the Cygwin cron service running automatically when I logged on to Windows 7. Here's what worked for me:
Using Notepad, create file C:\cygwin\bin\Cygwin_launch_crontab_service_input.txt with content no on the first line and yes on the second line (without the quotes). These are your two responses to prompts for cron-config.
Create file C:\cygwin\Cygwin_launch_crontab_service.bat with content:
@echo off
C:
chdir C:\cygwin\bin
bash cron-config < Cygwin_launch_crontab_service_input.txt
Add a Shortcut to the following in the Windows Startup folder:
Cygwin_launch_crontab_service.bat
See http://www.sevenforums.com/tutorials/1401-startup-programs-change.html if you need help on how to add to Startup. BTW, you can optionally add these in Startup if you would like:
Cygwin
XWin Server
The first one executes
C:\cygwin\Cygwin.bat
and the second one executes
C:\cygwin\bin\run.exe /usr/bin/bash.exe -l -c /usr/bin/startxwin.exe