Do you really use Putty to connect from an Ubuntu machine to an Ubuntu server? This is a highly unusual choice, I wasn't even aware Putty runs on Linux (turns out it actually does and even is in Ubuntu repositories).
A more conventional approach is to use ssh command from openssh-client package, which is a native implementation of a client for OpenSSH protocol. Install it with
sudo apt-get install openssh-client
Then you can connect to a remote machine with
ssh username@host.com
If you enable X11 forwarding with the -X switch, you'll be able to run applications on the remote machines and have them displayed on your local machine:
ssh -X username@host.com
Since you are running an proper real X server, you don't need to run xMing or anything like that.
Although, I agree that this is a solution for a strange problem - if you want to just edit text files, much more efficient options would be:
find a text-mode editor which suits you. I personally prefer Midnight Commander's editor which you can run with mc -e myfile.txt.
somehow mount the remote directory and edit files in your local text editor (using sshfs)
in KDE you can directly open a file from a remote host in any program using fish:user@host/path/to/file.txt. I think Gnome also can do something similar
make a local copy of the files, edit local files and use rsync to upload the changes
use a version control system