Let's say Failed to establish a new connection: [Errno 111] Connection refused is being returned when attempting to connect to a Windows host.

~]$ ansible all -m win_ping -i win_hosts.yml 
server1.example.com | FAILED! => {
    "changed": false,
    "msg": "basic: HTTPConnectionPool(host='server1.example.com', port=5985): Max retries exceeded with url: /wsman (Caused by NewConnectionError(<urllib3.connection.HTTPConnection object at 0x7f98e4707a10>: Failed to establish a new connection: [Errno 111] Connection refused',))",
    "unreachable": true
}

Often, this is because the winrm (Windows Remote Management) service is stopped on the Windows host. On the Windows host, PowerShell can be used to determine if the winrm service is stopped or running. If stopped, check out my article The WinRM client cannot complete the operation within the time specified.

PS C:\> Get-Service WinRM

Status    Name     DisplayName
------    ----     -----------
Running   winrm    Windows Remote Management