I used to use fairy liquid and then make a really watery chalk mix and stick it in that just before leaving for the show. Also put baby oil in overnight if you don’t want to plait or bag, nothing will stick to it!
also if the horse in question is grey, turnout rugs will be your best friend before a show. Waterproof so no nasties can soak through.
I soak the tail in a bucket of hot water and spray polar white into the bucket too. Then wash with fairy. I also find for in between washes if I spray a conditioner on the tail it makes it too slippery for the mud to stick to.