It appears Microsoft are to introduce "Windows Terminal", see https://devblogs.microsoft.com/commandline/introducing-windows-terminal/ It appears that you will be able to programme in C.
I was thinking of installing either MinGW or Cygwin so that I could write some programmes in C. Will the introduction of Windows Terminal make these redundant?
As Seva Alekseyev indicated, you don't need a terminal program to write C programs. You also don't need Cygwin or MinGW to write them. However, to answer the question that was asked, it appears that the new Windows Terminal will allow you to launch various shells. I'm hopeful that Cygwin will be among them. Note, however, that the new Windows Terminal appears that it will only work on the latest Windows 10 builds. In which case, you might consider WSL or even WSL 2 (also slated for later this year), which probably will be a much better environment for you than Cygwin or MinGW.