I prefer NOT to tie my McCarty tail to my saddle via the horn or front saddle string. It defeats part of the purpose of having the lead.
I prefer it in my belt loops or down my pant leg.
Depending on the diameter of your McCarty and belt loops sometimes putting it through two belt loops solves it from slipping, also material will have a factor.
However, don't stuff it through so many belt loops that you're welded to your lead and horse!
Another simple solution is using a thin piece of latigo leather to make a mock saddle string on the dee ring for your breast collar/plate.
If something bad happens the idea is the latigo will break rather than jerk a dee out of your saddle or possibly strand and ruin your mcCarty.
I DON'T LEAD 'EM AND FEED 'EM, I RIDE 'EM AND SLIDE 'EM.