Forms don't cookie leads. Munchkin does. If you have Munchkin on your external pages, you should be okay in regards to cookies.
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While, as Jim said, Marketo-hosted forms do not directly set cookies -- there are in fact situations in which Forms 2.0 actions are *intended* to set the Munchkin cookie, but the underlying code is buggy -- this may not be what you're asking.
If you wish an external form submission to associate the Munchkin session with a known lead instead of remaining anonymous, you have three approaches:
1. Submit a hidden Marketo form alongside your external form (recommended, easiest)
2. Call the Munchkin API associateLead method (more programmer-y, requires a developer though quite easy if you have one)
3. Use REST or SOAP API methods (not recommended unless you can prove beyond a reasonable doubt that 1. and 2. are unattainable in your environment, which is unlikely)