Can we customize user login block in Hybridauth module
There are two template files used 

hybridauth_widget.tpl.php 

This one is used to create the list of the icons. It gets a variable called $providers which has all the enabled providers. 

hybridauth_provider_icon.tpl.php

This one is used to print the individual icons. Two variables are used here. $provider_name is the name of the provider like facebook twitter etc. and $icon_pack_classes which has the current selected icon pack classes.

These template files can be found in with in the templates folder of the module.

You can make copy of the same in your theme and make the required changes.