My first horse came with a really pathetic excuse for a halter. I still have it, when I sell her, I'll offer it with her. I wouldn't give away her good halter. Just like I am sending her to a trainer shortly, obviously I'll send her in a functional, sturdy halter but it won't be her good one, that way if something happens to it, I won't be upset.
Always bring a halter and leadrope when you pick up a new horse. My last one came home in a halter and dog leash. Remembered to bring a couple different halter sizes, forgot the lead rope!