Cookies and cache

OK, so I haven't read every piece of mail on this list ... 

Can someone answer this simple question:

If I make a request for a page with a Cookie header, is the result 
cacheable in a public cache ?

e.g. I pick up a cookie with path=/ from some org, then
get a GIF (which has no Set-Cookie, Expires now, Cache-control, etc.), 
can it be cached ?

I think I had misunderstood the mechanism somewhat; if I want to use
the cookie in a page, should I make that page uncacheable with Expires, 
Cache-Control, etc. ??

Andrew