Sync custom folder icon with Dropbox
Your icon files are stored in the .DS_Store file located in each folder.  This file is what contains the metadata of the folder including the custom icon, the icon spacing, etc.

What is a .DS_Store file?

Drop Box, does not sync this particular file.  According to their help guide .DS_Store is ignored:



This means that your custom icon won't get synced.  You will have to create the custom icon manually.