Custom template for fields in user profiles
According to Drupal's theme hook suggestions for Drupal 7 the following suggested template names are available:


field--field-name--content-type.tpl.php
field--content-type.tpl.php
field--field-name.tpl.php
field--field-type.tpl.php


The content-type in this case is user (I guess it means entity type really), so to theme fields just for user profile pages, your template should be called:

field--user.tpl.php


I've just tested that on a dev site and it works perfectly.