Create a updater (fetch files from a directory)

I am working on a project, which is a local "web app" that consists of a structure of html files which together feel like a application.

The point of existance of this application is that it needs to be local. Using a webserver would have been much easier, but that is not an option.

Those html files have information in them that need to be updated every now and then. Packing the entire application folder and sending it out to all colleagues (or even just the files that changed in form of a patch they can overwrite the main folder with) is not always practical, so I would like to make an updater that will download and apply the latest changes/files.

It does not have to be advanced, all it has to do is fetch new files from a webserver. Technically, dropbox would be the way to go for this, but since this will be used on business computers and get dropbox installed on all of them just for the purpose of updating my app is not an option.

I am thinking of something simple, it does not even need to have a VB interface. A simple batch file in c++ would suffice. Something more advanced would be version check and only download and replace the recently changed files, but even if the updater would download the entire directory and overwrite all files would be more than enough to achieve my goal.

I had c++ classes at university a few years ago, but my knowledge is pretty basic since I haven't used it since then. The programs we wrote were basic practice examples and we never attempted something as advanced as an updater.

I hope someone might lead me in the right direction with hints and examples so I can achieve this goal.