"...white or colored rain gloves tucked under off-side saddle billets with the finger tips forward and just showing in front of flap." Quoted by the NEA Sidesaddle Association.
Rain gloves are historically defined as crocheted gloves - usually of a cotton fabric allowing the rider to take better hold of the reins that would slip through leather gloves.
Just for fun - here is a picture of some antique crochet hooks.
A modern version of rain gloves..