You can do it, but generally speaking it isn't considered secure. If you Google for "authentication with cookies" you will find that
"How to steal Facebook Authentication cookies"[
^] is at number five, with actual instructions a fair way off the first page.
However if you can live with a lack of security, then adding "C#" to the end of the search string will get you to the mechanics - the exact one you need is dependant on how you are handling the rest of your authentication.
Google[
^]
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