This is by design, not something that you can easily change.
Cookies / authentication sent via HTTPS are not sent by the browser when viewing the same site via HTTP. The best solution is probably to redirect the user from the HTTPS page to the HTTP page that sets your authentication cookie.
Keep in mind that this unauthorized cookie sent in clear text over a wire opens up the possibility for your users to substitute and reuse attacks. This may not matter to your application.
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