I'm supposing you have permission in your external host for these operations. That said, you have two approaches:
Using the mysqldump of your Windows MySql installation and a bat script for scheduling
If you have wamp/lamp/etc installed on your windows machine, you can use mysqldump in a bat file and set windows scheduler to call it everyday at 0:00 AM.
Create a .bat file containing: (Make sure that your output directory is writable for this task in Win Vista and 7):
set DATET=%date:~-4%_%date:~7,2%
"c:\xampplite\mysql\bin\mysqldump" --host="YOUR_HOST" --user="YOUR_USER" --password="YOUR_PASSWORD" YOUR_DB > "c:\"backup_%DATET%_YOUR_DB.sql
pause
...and set a task in your windows scheduler to call this bat everyday.
If you need additional parameters to your backup, don't forget to check mysqldump reference.
Using a "full-blown" software based backup solution
Check Mysql's solution directory. The only free solution I know of this list is the app from topsoft but I haven't tested it. You could check Sourceforge as well.