Is there an expression for the case when someone receives an email from a recruiter with whom he had no previous contact? I am looking for a term other than headhunting, like salesman knocking on cold doors, as it's said in other languages.
"Cold calling" is the usual term (in the U.S. at least) for an unsolicited contact by a person offering goods or services; the call could be an in-person visit, a phone call, or an e-mail. In the context of mail, the message itself could be referred to as "junk mail" or "spam", and the act of sending it is "spamming". This is usually used in the context of a mass mailing, but even narrowly-targeted messages, if unsolicited and unwanted, can be so labelled.
As FumbleFingers said, the act of "headhunting"; that is, attempting to recruit candidates for a job offered by a third party, is almost always initiated in a "cold" manner; the person doing the recruiting often has no pre-existing personal or professional relationship with the person they are attempting to recruit. So, the term "cold headhunting" is redundant; "headhunting" normally would suffice.
I've always been under the impression that "headhunting" is normally "cold" in OP's sense.
A reasonable definition of headhunting is that it's the practice of approaching someone who is already employed at another company. To my mind, unless that someone has put his name down with a recruitment agency, any approach he might receive is by definition "cold calling".