It's pretty simple: Directory.GetFiles has an overload which accepts a pattern:
string files = Directory.GetFiles(@"D:\Temp\", "*.jpg");
You can then use File.Move as before.
But you do realize that changing an extension doesn't magically make it readable as the new extension, don't you? That an "AVI" file is still a video file even if you rename it's extension to "DOCX"? And that Word won't be able to open it?