The only website that can read a cookie is the one that creates it. Also, web servers are only able to use the information you provide, or choices that you make as you visit the website as their content in cookies.
Cookies make it simple for websites to track access.
When you accept a cookie it does not give a server access to your PC or any of your personal data, unless you have given this information, for instance when shopping on line. Servers are only capable of reading cookies that they have set, this way other servers have no access to your information. Cookies cannot execute code, therefore it is not possible for cookies to deliver viruses.