Putty usually comes with the "plink" utility.
This is essentially the "ssh" command line command implemented as a windows .exe.
It pretty well documented in the putty manual under "Using the command line tool plink".
You just need to wrap a command like:
plink root@myserver /etc/backups/do-backup.sh
in a .bat script.
You can also use common shell constructs, like semicolons to execute multiple commands. e.g:
plink read@myhost ls -lrt /home/read/files;/etc/backups/do-backup.sh