|No, there is no way you can see what is on a web site without going through the web server and downloading whatever the web site owner wants you to download and the cookies with it. The chances are the cookies do not actually exist as a file but are generated by code when the relevant page is requested. To see if you are going to get any tracking cookies you would need access to the server scripts which no sane web site owner would allow.|
You can take it as read though that any site that uses adverts, like this one, is also going to be sending you tracking cookies. They are an unavoidable fact of life if you use the Internet.
However a good application like Crap Cleaner will soon get rid of them: