Back on track has good quarter sheets!
They make blankets for this
a rain sheet with holes for the stirrup leathers. the one i use the most is the rambo mack in a sack rain sheet!
Waterproof riding blanket shiuld do the trick
Ride on rug. Comes I waterproof
Non turnout rains sheet. If you want you could cut a hole out for you and your saddle.
A waterproof quarter sheet would work! :)