How do I append a country to a views exposed filter field geofield proximity?
As with any form, a custom module can modify the #submit array to put a submission handler in front of the views exposed filter form to preprocess the data. 

Here we're just modifying the submitted origin value so that " Canada" is appended if any text is entered by the user: 

/**
 * Implements hook_form_views_exposed_form_alter().
 */
function MYMODULE_form_views_exposed_form_alter(&amp;$form, &amp;$form_state, $form_id) {
  array_unshift($form['#submit'], 'MYMODULE_form_views_exposed_form_submit');
}

/**
 * Modify submission value if given origin has been supplied.
 */
function MYMODULE_form_views_exposed_form_submit($form, &amp;$form_state) {
  if (isset($form_state['values']['field_geofield_distance']['origin']) &amp;&amp; 
      strlen($form_state['values']['field_geofield_distance']['origin']) &gt; 0) {
    $form_state['values']['field_geofield_distance']['origin'] .= ' Canada';
  }
}