In the MLB.com At Bat app, users can customize the Home screen icon of the app with MLB club-branded app icons representing their favorite team. Similarly, in the NHL app, app icons can also be customized with team logos instead of the standard NHL app icon.
To change the icons, iOS 10.3 is required. Subscribers can go to More --> Settings --> Home Screen icon and choose a team logo.
As TechCrunch points out, while developers are now able to change app icons without pushing a full iOS update, there is no support for dynamic app icons that would allow for things like a weather app icon that updates continually with the temperature.
Customized Home screen icons, which Apple calls "User-Selectable App Icons" may be something that we'll see a lot more of now that iOS 10.3 is available to the public. Apple has strict rules for icon customization options, requiring visual consistency, a simple icon swap interface, and explicit user permission to change an app's icon.
MLB.com At Bat can be downloaded from the App Store for free. [Direct Link]
NHL can be downloaded from the App Store for free. [Direct Link]