Cookies are only sent to servers that created them so other servers will not see them. There is an exception to this. If several servers are load balancing a site, cookies created on one can be seen by the other servers because they are all in theory the same site.
If you're coding in CF, I would use CF's cookie handling features as they do a lot of the decoding work for you that you would have to do manually in Javascript. Just use <cfset x = cookie.var1> to get a cookie called "var1". In javascript, cookies are accessed by the document.cookie object and I believe it returns one long string containing all cookies and values which you have to split up and parse out yourself.
Hope this helps,
GJ