TLS 1.0 is disabled by default in Mule 3.9 and Java 1.8. You only will have an issue if your applications try to connect to any HTTPS service that only accepts TLS 1.0. Those will reject your HTTPS requests.
If those services exposing only TLS 1.0 are APIs or are not APIs, that's irrelevant as we are talking about HTTPS as a communication transport and what they are doing doesn't change that. It may be plan HTTPS or a SOAP web service behind HTTPS.
Anypoint Platform has deprecated TLS 1.0 for some years so any platform APIs and the global load balancers will reject TLS 1.0.