My Lumia 735 with Windows 10 Mobile (Version 1607, Build 10.0.14393.1593) has a native emoticon supply accessible via the smiley button on the keyboard.
Those emoticons are available for basically any app that allows keyboard input.
I did notice however, that the emoticon set is not the same as the one offered by Whatsapp. Some emoticons are either missing from the Windows set, or are not displaying correctly when sent via Whatsapp. I have the option of using both sets though, so not much of a problem.
Instagram for Windows Mobile for example does only offer my native emoticon set, and is therefore lacking its own set. Out of this issue arose the question, if it is possible to update or change the native Windows Mobile 10 emoticon set?