How to Hide search box

There are ways to hide the search box. 

1. If you can edit master page, just set ‘visible’ property of Serachbox control to false. (DONOT Edit OOTB SharePoint master page and may cause issues in other areas.)

<SharePoint:DelegateControl runat="server" ControlId="SmallSearchInputBox" Version="4" Visible="false"/> 

2. You can use CSS to hide the Searchbox by setting the display property to none. Add this to custom css file.

#s4-searcharea { display:none; }

If you want to hide search box in a specific page then you can use Content Editor webpart and place CSS code like this. 

<style>
#s4-searcharea { display:none; }
</style>