If you are able to control the method that the client connects to the SQL Server, and have control of the SQL Server, then it might be best to switch the server to SQL Server and Windows Authentication mode instead of just Windows.
However, if you require the clients Windows login in order to differentiate the users accessing the SQL Server, then you may be out of luck. If the SQL Server is configured to only allow Windows Authentication, then it will only accept connections from the Windows logins defined on the Windows server - if the server is in workgroup mode and not domain mode.
The workaround for this has always been to ensure that a Windows account exists on the client and server with the same name and password, but if you are now required to use a Microsoft Account (formerly known as a Live Account) as your Windows login on your desktop I don't see how you would give that account access rights on the SQL Server.