In iOS / Android:
- When you pin the app to the Home Screen, it will have the same icon that you have defined in the app. For example, I changed the icon in the App Settings for an app and saved it to PowerApps:

In the iOS, after I pinned it to the home screen, it will use the icon that was defined:

A similar behavior happens for Android as well
In Windows:
Currently there is a bug in the product that the icon is not being used when you pin the app to the Home / Start menu. It should be fixed in an upcoming version of PowerApps, and when this is done the icon will also be used in the Start menu.
Addendum: the Web player:
You can also "pin" the app pointing to the Web player. When you open an app in the Web player, it will have a URL that will point to the app (for example, my app's address is at https://web.powerapps.com/webplayer/app?source=portal&appId=%2fproviders%2fMicrosoft.PowerApps%2fapps%2f1f7a8f34-8e60-8f1c-eab0-c16ad58b0fad). The product itself doesn't have a "pin to home" functionality in the web player, but you can create an Internet Shortcut that points to that app, and place it anywhere (e.g., in the desktop), and change the icon in the desktop to be whatever you want. This would need to be done on a per-machine basis, so it's not very easy to do for a large number of machines, but it's doable.