third party icon not showing ie. snapchat

Apple advises that the issue of app icons not appearing in notifications on Apple Watch is addressed under iOS 11.1, released today.

watchOS 4.1 has also been released.

Follow the instructions here to update your iPhone and Apple Watch, starting with your iPhone and beginning by making a backup of your iPhone:

• Update the iOS on your iPhone, iPad, or iPod touch - Apple Support
• Update your Apple Watch - Apple Support

Hi

Some other users are experiencing the same issue.

I suggest that you let Apple know that you are also experiencing it:

Feedback - Apple Watch - Apple

I'm having the same issue. The Snapchat icon isn't appearing within the Photos app even though the OS is up-to-date and I rebooted as well. Maybe it's necessary to contact the developer?