HI Joyce, 
It's not currently possible to have different icons for a single activity, activity-level selection of icons is a great idea! Please submit it to the Suggest Features forum.

There is a workaround however, which we actually use on the Community site, you can see it in action on the Community course page in the  Totara Learn topic. You'll see a handful of discussion forums with icons next to them. These are all forum activities, but we've created different images to go with them. The way we do it is by creating an Orphan section at the bottom of the course page. Essentially you add a topic section, put something in it (an activity or resource) and then go to the Course Settings page and set the number of topics to be one less than what is displayed on the page. That last topic section will now be hidden from the learners, but the activities in it still exist. Then in one of the visible topic sections, add a label with an image and link to the activity using the HTML editor.

Hope that helps!

Wes