Disclaimer:
As stated earlier by @feroze, setting your cookies' domain to localhost is not going to work out so well for you. I'm assuming you're writing a helper that allows you to tunnel HTTP requests out to foreign domains. Note that this is not best practice and in a lot of cases is not needed (i.e. jQuery has a lot of cool cross-domain support built-in, also see the new CORS specification). But sometimes you may be stuck doing this (i.e. the external resource is XML only, and is on a server that doesn't support CORS).
Background Information on Cookie Domains and How They Work:
If you haven't already take a look at HTTP Cookie: Domain and Path on Wikipedia -- pretty much everything you need to know is in there.
When evaluating a cookie, the Domain and Path are taken into account by both the client (the "local" requester) and the web server (the "foreign" responder). When a client requests a resource, the client should only send cookies where those cookies match the Domain (or a more generic parent domain) and Path (or a more generic parent path) of the URI being requested.
Web browsers handle this correctly. If a web browser has a cookie for the domain "localhost" and you're requesting "google.com", for example, those cookies for the "localhost" domain won't be sent in the request to "google.com". -- In fact, most modern browsers won't just not send them, they'll completely ignore them in Set-Cookie response headers that they receive (these are called third-party cookies -- enabling the acceptance of third party cookies in your web browser is a huge privacy/security concern -- don't do it!).
It works in the other direction as well -- even though it's unlikely for a client to include a third party cookie in a request, if it does, the foreign web server is supposed to ignore it (and even some cookies for correct domains/paths, so as to prevent the infamous super-cookie issue. (i.e. The web server hosting "example.com" should ignore cookies belonging to its parent domain: ".com", because ".com" is a "public suffix")).
What You Should Do [if you have to]:
The course of action I recommend for you, is when you read in your client's cookies (I'm not an MVC guy, but in regular ASP.NET this would be in Request.Cookies), loop through them (make sure to filter out your own site's legitimate cookies, especially SessionId, etc -- or use Path properly so they never get sent to this page in the first place), then add them one at a time to the outgoing request's cookie collection, rewriting the domain to be "www.whatever.com" (per your example -- if you're doing this dynamically, load the URL into a new Uri() object and use the .Host property), and then set the Path to "/". -- This will build the "Cookie" header for the outgoing request to the foreign web server.
When that request returns to your server, you then need to check it's incoming response for new cookies -- those cookies can be repackaged and sent back down to your client in much the same type of loop as I illustrated in the previous paragraph, except you'll want to rewrite Host to be Request.Url.Host -- and you'll want to set path back to "/" unless the path to your passthru page is static (I'm guessing it isn't since you're using MVC) then you'd want to set it to Request.Url.AbsolutePath for instance.
Happy Coding!
EDIT:
Also, you'll want to set the X-Forwarded-For tag of the outgoing request, so that the website you're calling doesn't think your web server is one single client that's been spamming the crap out of them.