What is your version of budget friendly? And what kind of quality do you want/need?
The Dover Saddlery Suffolk/Crown leather halters are super budget friendly and have a snap throat and buckles on each side… I have some that are six and seven years old, been outside in NE in 24/7 weather and just don’t die. That being said I think they’re horribly hideous right out the bag, but my barn mates love them and they really are indestructible.
https://www.doversaddlery.com/dover-saddlery-padded-halter/p/X1-05246/
I don’t like halters with the hanging o-ring at the chin strap, so I prefer english-chin style halters (like below). Totally preference based and not as budget friendly.
https://www.doversaddlery.com/finntack-american-lthr-hltr/p/X1-05476/
My show halter is a Perry’s and it’s just stunning in person. It was not cheap ($150 MSRP) but SO won it in a raffle. They come in pony and cob sizes.
If you wait until closer to Christmas, Dover’s Suffolk and in-house brands always go on sale for half their list price and you can get one of those halters for $20.