Are your contacts backed up? If so, go to Settings >Applications >Application Manager>All. Then scroll down to Contacts. Tap on it then tap on disable. Wait till it finishes then enable. That should bring your icon back.
You asked about changing icons. If you are using Nova Launcher, download Moonshine Icon Pack from the Play Store. There are dozens of icons there to change out with original ones. As far as I know you can't change icons on the built in Launcher. With Moonshine you press on the icon you want to edit. You'll get a pop up option to edit, remove, uninstall. Tap on edit. A new pop up will appear. You can now change the name and if you press and hold the icon it will take you to all the available icons on you phone. Just choose which one you want then tap the check mark on the pop up and you're done. Also with Moonshine you can select a new calendar icon and the date will change daily instead of it always showing the 31. Nice little feature. Developer very good responsive to questions.
Hope this helps.
Posted via Android Central App