What cannot be used through SSH/PuTTY is the IDE that you're comparing text-only Vim to.

One that runs on X can be tunneled.

It works independently of transmission method since the mouse clicks are simply translated into "keyboard presses", i.e. encoded to stdin as escape sequences. It's a single stream.

Of course, the terminal emulator must play nice with the windowing environment and translate mouse events correctly.

It works through PuTTY, and moreover it's the default config in Debian 9, which I find sort of annoying because I'm used to using the mouse in PuTTY for copy/paste. But it does work smoothly (including through a screen session and through ssh to other machines).

Perhaps you should add an [edit] to your original post seeing as it's nabbed top spot and spawning several threads about lack of cursor support?

Not sure about putty but it definitely works over SSH depending on your terminal emulator.