D7 Webform tokens for user fields
It appears that this can't be done using the standard webform module. It defines a limited list of tokens that hasn't been updated for the new user fields. They are included as tokens (if you use field_nnn) but they will be an empty value. 

After initially looking at building a custom module, it seems that the Tokens module does make user fields available in the form [user:field_nnn].