Is the balance of my account cleared if I delete my cookies?

No, the balance of your account is not stored in your browser but in the Nimiq blockchain. The browser only stores the access to the funds for you. This access is stored in the browser offline data. Thus, the access gets only lost when the browser deletes the offline data, not by deleting the cookies. Nonetheless, it's important that your always backup your account access via Account Access File or 24 Recovery Words.