Is there a convention for the case of the file extension in Windows, i.e. all uppercase vs. all lowercase? If there is, what is the reason, if any, for the convention, or is it just for the purposes of uniformity?
Windows is intentionally case-insensitive (by default) when it comes to file names and extensions. It doesn't matter what casing you use.
This was a primary design decision that Microsoft made previous to Windows in their original OS (MS-DOS) and file-system(s), to separate themselves from Unix. It was touted as one of the reason MS-DOS was "easier to use".
The original FAT file systems actually stored the files names (and extensions) as all caps, regardless of how you entered them (making it 'case-insensitive', but not 'case-preserving').
Perhaps check out this related SU question: Are all versions of Windows case insensitive?
There is no convention. Windows is case insensitive by default. This means file.txt, file.TXT, file.Txt. file.tXt, ... are all the same file name. Note, this is not the case for UNIX or Linux, where the previous list of files are unique filenames.
FYI, you can make Windows case sensitive, but thats off topic for this question.