I'm guessing that if you refer to the default field in relation with the user, you're using Commerce Addressbook, you've got an api function to get the default profile given a user id and the profile type: commerce_addressbook_get_default_profile_id
If you're not, you can get the profiles used by a given customer using the customer profile reference field for billing / shipping / whatever and consulting the variable commerce_customer_profile_' . $type . '_field'
So for loading the profiles of a given type you can use Entity Field Query using the customer user id against the order entity.
$query = new EntityFieldQuery();
$result = $query->entityCondition('entity_type', 'commerce_order')
->propertyCondition('uid', 0)
->execute();
if (!empty($result['commerce_order'])) {
$orders = entity_load('commerce_order', array_keys($result['commerce_order']));
}
And then wrap the entity or use field_get_items:
$field_name = variable_get('commerce_customer_profile_billing_field', '');
$order_wrapper = entity_metadata_wrapper('commerce_order', $order);
$order_wrapper->{$field_name}->value();