How can I search for a contact by its phone number? Is it possible to search for a contact by phone number in Froyo ? How ?
HTC's Sense UI gives you this functionality out of the box.  In the Phone app if you start typing the phone number, it will filter your contacts that include either that number, or the contact's name via T9 representation.

If you are not running Sense IU, I suggest trying 3rd-party apps that imitate the HTC Dialer functionality.  Try Dialer One or aContacts, for example.