End of Life? Dude, I'm running Cobol code that probably dates back to before you were born!
If it does the job that's one thing. If it's all patched and up to date security-wise, you are OK. If however, the systems are constantly running at 100%, and you've got latency and throughput issues, then that's a different story.
If nothing's getting backed up because the systems are under huge strain, then in that case you are welcome to start upgrading. In fact, you might be able to keep the same hardware and simply "upgrade" to Linux slowly, which is less resource-intensive than Windows.
And the way to do it is to build a new box that "mirrors" an existing one; once you've tested it to death, and you're confident nothing has been missed, you retire the original box, then use that box for the next build that mirrors another box and so on.