Is it possible to track a private ip address?

What type of tracking are you talking about? It matters... a 10 series is typically a local subnet.. but you can't get to the outside world with that... it has to be translated to another outside address... THAT can be tracked...

Of course with Cookies they can also track a number of things depending on how malicious they are.

IP adresses in the range 10.0.0.0 to 10.255.255.255 are reserved for use inside private networks, and hence info about the machines using these IP addresses are not made public to the rest of the world. However, if you are logged into the network you may be able to use an IP scan utilty such as "AngryIP" to see what machine this IP is assigned to. One word of caution - in most networks IP addresses are assigned dynamically by a Dynamic Host Configuration Protocol (DHCP) server, which means they can change when a user logs in or out, so the machine assigned this particular IP address today may not be the same machine that had it yesterday.

BUT... the internet provider does have logs as to who was assigned a specific ip at any given time... but only a court subpoena generally gets them to part with it.

ISP logs won't help with a private address.

Why do you want to know?