First off, a primer on calling single extra fields...
=== Call specific extra fields in K2 templates ===
To directly output individual extra fields in your K2 overrides, do something like this (e.g. in item.php) to get the extra field name:
echo $this->item->extraFields->EXTRAFIELD_ALIAS_HERE->name;
To get the extra field value you would simply do this:
echo $this->item->extraFields->EXTRAFIELD_ALIAS_HERE->value;
echo $this->item->extraFields->EXTRAFIELD_ALIAS_HERE->rawValue; // for date type only
Simply replace EXTRAFIELD_ALIAS_HERE with the actual alias of the extra field you wish to output.
In modules, use:
echo $item->extraFields->EXTRAFIELD_ALIAS_HERE->value;
echo $item->extraFields->EXTRAFIELD_ALIAS_HERE->rawValue; // for date type only
Now that you know how to call a specific extra field, you can simply wrap that field with some PHP code that checks if a user is logged in, e.g. (for the item view):
// Get user instance (if any)
$user = JFactory::getUser();
// Check if user is NOT a guest, then show the extra field
if (!$user->guest) {
echo $this->item->extraFields->EXTRAFIELD_ALIAS_HERE->name;
}