First thing to do is to go to Template > Edit HTML and then search for the gadget's code we want to hide. It will be easier using the CTRL + F keys and locating the name of the gadget/widget.
<b:widget id='HTML1' locked='false' title='' type='HTML'>All you have to do is add the parts in red and ready. If you close the session go to your blog you'll not be able to view the gadget that you have hidden, but as soon as you sign in you will see that it is visible to you.
<span class='item-control blog-admin'>
<!-- only display title if it's non-empty -->
<b:if cond='data:title != ""'>
Not all gadgets have the same structure like in my example, but it will be easier to guide you, just place the first code in red just after <b:includable id='main'>
And the second red code just before </b:includable>
Note: to look inside the widget's code, click on the sideways arrow next to the widget's id.
And with that the gadget will be hidden for readers except you.