How can I set folder permissions for elastic beanstalk windows application?

This is already possible since April 2013, see also here: Basically the steps you need to perform are the following:

1. Create a folder called .ebextensions in the top-level of your project through the solution explorer
2. Add in this folder your configuration file e.g myapp.config (replace myapp with your Elastic Beanstalk's app name)
3. Add the code displayed underneath to this configuration file you just created. Replace MyApp with your project name (not solution name) displayed in Visual Studio

4. All set!! Be sure there's a file within App_Data otherwise Visual Studio won't publish it.

   {    "containercommands": {        "01-changeperm": {            "command": "icacls \"C:/inetpub/wwwroot/MyApp_deploy/App_Data\" /grant DefaultAppPool:(OI)(CI)"        }    }}

To give write permission to your DefaultAppPool you can
create an .ebextensions folder
create a config file and place it in your .ebextensions folder

This will change permission to your wwwroot folder

container_commands: 01-changeperm :  command : 'icacls "C:\\inetpub\\wwwroot" /grant "IIS APPPOOL\DefaultAppPool:(OI)(CI)F"'

I had the same problem (unable to write to a file in the App_Data folder of my web application on Elastic Beanstalk).

In my case it was sufficient to create a dummy file in the App_Data folder in my Visual Studio project. When I did this, the App_Data folder was created during deployment with permissions that allow the web application to write to it.

No need for .ebextensions to change folder permissions.