The Cookie Container class is not present on the .net Compact Framework.
However, http cookies are just http headers.  You can manage the headers
yourself in order to keep session state with the server.  I believe there is
an effort in opennetcf.org to retrofit a CookieContainer to .NET CF v1.1.  I
don't know the status.  See:
http://www.google.com/search?num=30&hl=en&lr=lang_en&q=cookiecontainer+site%3Aop
ennetcf.org

Another way to do it is to "roll your own" session management, not depending
on HTTP Cookies.
Add an initial method that the client calls;  when the server receives this
call, it creates a state instance, and returns a "handle" to the client,
maybe an Int32.  The client then just passes that handle in all successive
calls.

This is basically the way a Google or Amazon webservice works today, If I am
not mistaken.

When the client is "done" with the conversation, it can call a Close()
webmethod.
You'd still need to expire server-side state resources in case the Close()
is never called.

also see here:
http://www.google.com/search?num=30&hl=en&lr=lang_en&q=%22web+services%22+%22Ses
sion+management%22

-D