Domain set cookie for subdomain

No. Besides that fuu.example.com is an invalid Domain value (it must start with a ., i.e. .fuu.example.com) (see update below) the cookie would get rejected:

To prevent possible security or privacy violations, a user agent rejects a cookie (shall not store its information) if any of the following is true:

• The request-host is a Fully-Qualifed Domain Name (not IP address) and has the form HD, where D is the value of the Domain attribute, and H is a string that contains one or more dots.

The request-host is example.com and the Domain attribute value is foo.example.com. But the request-host example.com does not has the form HD where D would be foo.example.com. Thus the cookie gets rejected.

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Update    The current specification RFC 6265, that obsoleted RFC 2109 that is quoted above, does ignore the leading dot. But the effective domain is handled the same:

[…] if the value of the Domain attribute is "example.com", the user agent will include the cookie in the Cookie header when making HTTP requests to example.com, www.example.com, and www.corp.example.com. (Note that a leading %x2E ("."), if present, is ignored even though that character is not permitted, but a trailing %x2E ("."), if present, will cause the user agent to ignore the attribute.)

[…] the user agent will accept a cookie with a Domain attribute of "example.com" or of "foo.example.com" from foo.example.com, but the user agent will not accept a cookie with a Domain attribute of "bar.example.com" or of "baz.foo.example.com".

Actually, there is a simple and fully cross-browser support way for sharing cookies between original domain and subdomains but you should share it in setting time, for comfortable working with cookie stuffs in browser I'm using js-cookie and with the below setting cookie it could be shared between original domain and all of its subdomains:

Cookie.set('key', 'value', { domain: '.domain.com' })

// a . added before domain name

Hint: Adding this . will share cookie with all sub-subdomain.

The 2 domains example.com and foo.example.com can only share cookies if the domain is explicitly named in the Set-Cookie header. Otherwise, the scope of the cookie is restricted to the request host.

For instance, if you sent the following header from foo.example.com:

Set-Cookie: name=value

Then the cookie won't be sent for requests to example.com. However if you use the following, it will be usable on both domains:

Set-Cookie: name=value; domain=example.com

In RFC 2109, a domain without a leading dot meant that it could not be used on subdomains, and only a leading dot (.example.com) would allow it to be used across subdomains.

However, modern browsers respect the newer specification RFC 6265, and will ignore any leading dot, meaning you can use the cookie on subdomains as well as the top-level domain.

In summary, if you set a cookie like the second example above from example.com, it would be accessible by foo.example.com, and vice versa.

For more details : https://stackoverflow.com/a/23086139/5466401