You have to own a unicorn, then there will be a link on its page to remove the horn. The uni then becomes a regular horse.

Sounds permanent.

It is, unfortunately,

If you have to buy a Unicorn for this kind of Objective, the cheapest ones are always colts. You can always send it to the Safe Haven after you de-horn it, and get back 2000e (as long as neither parent has been de-horned, too). You do lose some equus, but then again you gain some passes.

If you breed Unicorns, even casually, you can keep back a few colts for this kind of Objective. You don't have to work them or board them, after all. I breed Unicorns, so I always have a lower-GP colt around that I don't need to BLUP or breed and can use for this.

You can also either skip the Objective and only complete one that day, *or* pay the equus to swap that Objective out for a new one.