Barman can backup a Windows host but restoration is more complicated. There are several problems here:
Tablespace directories get screwed up because of different path semantics This is true whether the directories are stored on Linux or on Windows via NFS (the only way of getting around the path semantics issue on restore)
Barman restore assumes the presence of UNIX file and other utilities that do not exist on Windows, including true, mv, and others.
The first would probably be fixed by some sort of normalization of paths before storing tablespaces (or of just handling the differences). This requires an actual effort to port the application to Windows, though.
Barman can backup a Windows host but restoration is more complicated. There are several problems here:
The first would probably be fixed by some sort of normalization of paths before storing tablespaces (or of just handling the differences). This requires an actual effort to port the application to Windows, though.