This depends on how you are displaying the video. From your question I gather that it's from the node view. The first comment from Djouuuuh is correct, but this is very time consuming and understandably may not be an option for you. So I'll tell you how you can make it work in a smaller time frame with some templating.
First you need to make sure the video field and the thumbnail for the video are available to the display. If you have a thumbnail field that gets populated automatically or uploaded to manually then all you have to do is add that to the display.
Go to admin/structure/types/type/manage/display and make sure the display you are trying to edit has both fields. If your thumbnail field is on the video entity then all you would need is the video field. Also, install and enable the devel module so you can test your displays.
In your node--type.tpl.php template you would need to first test that you have the data available to you, so write at the top of the document, flush cache, flush browser cache, and reload the node page. Click through the message printed at the top to make sure you have the data you need.
If the data is there, then you can start doing some templating to get the node to look how you want with the preview. One quick solution I can think of is to utilize HTML5's tag with the placeholder attribute.
Something like this:
<?php
if (isset($content['video_field'])) { $video = $content['video_field']['und'][0]['link_to_video_file']; }
if (isset($content['video_field']['und'][0]['thumbnail']['link_to_thumbnail_file'])) { $thumbnail = $content$content['video_field']['und'][0]['thumbnail']['link_to_thumbnail_file']; }
?>
<div class="video-wrapper">
<video src="<?php if (isset($video)) { print $video; } ?>" poster="<?php if(isset($thumbnail)) { print $thumbnail; }?>"></video>
</div>
There are other attributes in addition to poster you can use with the tag to embed controls, timers, multiple video file type sources, etc.