You can also mount Linux file systems through SSH. This is called SSHFS. This solution will be preferable if you are not willing to set up anything on the Linux servers. In Windows there are alternative clients to do this, like this one. With new Windows and Linux versions Windows clients sometimes break up, but you can try it anyway.
Another alternative you might want to consider is setting up public key authentication, so that WinSCP would be more integrated to your Windows environment. There is a guide for public key authentication here. However this does not give you perfect integration, you can not see remote file system in "Open File" dialogs provided by Windows.