Replace cortana icon with search icon in Windows 10 v1607

To disable Cortana and get the old search icon back, start regedit.exe, go to HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Windows\Windows Search, create a new 32-bit DWORD value here named AllowCortana and leave its value data as 0.

After a reboot you see the Cortana Logo is gone and the local search opens:

Since Windows 10 v1803 (Build 17134) you also need to add the DWORD BingSearchEnabled and CortanaConsent to 0 under the mentioned key.

Windows Registry Editor Version 5.00

[HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows\CurrentVersion\Search]
"BingSearchEnabled"=dword:00000000
"CortanaConsent"=dword:00000000