I am a “bareback” mare and I do not want ANY of the stallions to use a condom with me. Is this all right?

Clearly NO!

The mares may offer some unprotected sex, but they cannot be “bareback only”!
In other words, “bareback mares” have to take any stallion, with or without a condom.

Violation of this rule leads to a ban from the Horse Fair !!!