Wiping down your tack after every ride is essential for the longevity of your saddle, girth, bridle, and all other leather parts! If it is made of leather, sweat and dirt will erode it over time. A quick wipe down also prevents sand from scratching the leather, and in more humid climates an anti-mildew formula can be used.
Effax makes a very nice leder-combi daily cleaner/conditioner for a quick and easy wipe down, and they make a mildew formula in a spray bottle too. But even a damp, clean cloth is fine! The important thing is that you remove the dirt, sweat, and excess moisture before putting away your tack. Plus, it makes your weekly deep-clean and condition a lot easier!