How to change footer or for different kinds of users in wordpress?

When a user is logged in, WordPress adds the class logged-in to the body tag, so you can target CSS differently for logged in users.

body > footer {
    background: black;
}

body.logged-in > footer {
    background: red;
}

for example.

This is only good for cosmetic changes though. Don’t try to use it to hide information from non-logged in users as the content is still in the HTML.