Thanks for the follow-up Jesper Andersson! I will try to take a look
Note that it's possible to fix this without modifying WinSW itself. You can add:
<AppContextSwitchOverrides value="Switch.System.Net.DontEnableSchUseStrongCrypto=false"/>
to the <runtime> section of jenkins-slave.exe.config. This will enable TLS 1.2 (and disable SSL 3.0) if WinSW is executed with .NET Framework 4.6 or later.
https://github.com/jenkinsci/jenkins/pull/4010 is a PR against the core.