I'd imagine the symptoms were also reduced. Cold showers reduce inflammation, so I'd imagine people who practice them would feel less miserable once the 'fight it off' portion of the infection is over.
My doctor also recommended cold showers (or at least ending with a minute of cold) as a means of stress management. Apparently it stimulates some nerves and reduces the stress damage somewhat. Possibly related to lower inflammation too. Anecdotally I do feel better when I do it and miss it when I don’t.