The only way to find out is to call the haulers. You can get a ball park figure by calculating what it would cost you to go get the horse. Sometimes its' less, sometimes it's more for a commercial hauler. I usually found it was less as I got older as I had to stop more frequently and couldn't drive as many hours/miles before having to stop for the night in a hotel/motel.
I've had some tell me that you can find "deals" with U ship it. Think that is what it was called. I never got that to work.
You can also see if the mini could "hitch a ride" with folks going to/coming from AMHR/AMHA shows. Post an ad on the sales board above and also in the "Wanted" forum here to see what folks might be hauling empty one way and could pickup/haul for you. You'd be surprised.
I had 1 mare from the west coast make two "farm hops" with 2 different haulers going to shows, then I picked her up in the mid-west after meeting with 2 others to pick up ponies. Had a total of 7 ponies that we picked up coming in from 3 different states - picked 1 up in NE, a 2nd up at another farm in IA and the rest all met at the last farm (that we purchased the balance of the ponies from) for us to take them home. Boy, that brings back some memories!!
Another time I had another mare also come from the mountains on the west coast and come all the way here to NC on one haul (Sharrway Transport - no longer in operation). The last time I had a mare/foal transported from the West - hitched a ride to the AMHR Nationals, I paid for a stall there, then got a ride to a farm KY and that person brought them on to me a bit later.
I've transported others for folks one way when I went to pick up one of my own! That paid for at least part of my trip quite a few times. Of all of the ponies I've sold over the years, I've delivered about 1/2 of them. Yes, I get at least gas money. In 2012, I purposely put ponies in training with trainers in states I knew I'd be visiting for family. Made numerous trips to different states - each time visiting my ponies either at the trainers' farms or at shows to watch them show - and various family members thru 2012 AND 2013 into 2014. My family wants to know when we are doing it again... probably won't happen again any time soon due to our own health issues and $$ and my job change, but you never know.