From a powershell prompt, use the gci cmdlet (alias for Get-ChildItem) and -filter option:
gci -recurse -filter "hosts"
This will return an exact match to filename “hosts“.
SteveMustafa points out with current versions of powershell you can use the -File switch to give the following to recursively search for only files named “hosts” (and not directories or other miscellaneous file-system entities):
gci -recurse -filter "hosts" -File
The commands may print many red error messages like “Access to the path 'C:\Windows\Prefetch' is denied.“.
If you want to avoid the error messages then set the -ErrorAction to be silent.
gci -recurse -filter "hosts" -File -ErrorAction SilentlyContinue
An additional helper is that you can set the root to search from using -Path.
The resulting command to search explicitly search from, for example, the root of the C drive would be
gci -Recurse -Filter "hosts" -File -ErrorAction SilentlyContinue -Path "C:\"