Shipping companies can charge anywhere from .50 cent per loaded mile up to $2.00 a loaded mile. So the cost could range anywhere from $1,000 to $4,000 or more, in just mileage/gas. But you also have to take into consideration MANY things when shipping a horse thousands of miles:
1) this is a multi-day trip. 2,000 miles in a passenger vehicle with just people driving would take 30 hours. If you're driving 8 hours a day, that's 4 days roughly and that's at posted speed limits of 70mph (or more) roughly. A commercial hauler will probably average 60mph or less and cover waaay fewer miles in a day. I'd say it's a weeks trip, minimal
2) since it's at least a week to cover this much ground, where does the horse stay every night? who makes the arrangements?
3) all arrangements for overnight stays are probably extra.. I'd bank on at least a couple hundred or more extra.
4) hay? water?
5) legally, many states require that you get a certificate of health EVERY time you cross state lines. now, I've never shipped a horse cross country so I don't know how this is handled but I would imagine a reputable company would indeed follow the laws of the states they're crossing. For me, locally, my vet charges about $100 for a health certificate... so, let's say you're shipping from Michigan to Nevada. That's 8 states you're crossing, and $800 extra dollars in vet fees, minimal.
now I'm just guessing at all of this because, like I said, I've never shipped a horse across the country and hey, maybe none of what I'm saying applies at all. But I know I wouldn't feel safe with a company taking possession of my horse without following every single precaution that they could, including hay, water, overnight arrangements and health certificates as this is what I would do if I was personally hauling my horse across the nation.
Honestly, though? I've heard nothing but horror stories when people use commercial companies to ship their horses. I mean, honestly, really horrible stories of shipping companies. I wouldn't trust any of them - not even the "highly rated, highly recommended" ones because those, as well, have horror stories. I've heard of companies delivering DEAD HORSES to people.. horses that were clearly alive when they got on the trailer but somehow didn't make it.
If you're absolutely set on getting this horse, I would either figure out a way to pay for him where he's at, save up money and buy a truck and trailer, or find a friend or somebody you can trust personally to haul him to you. I own a truck and a trailer so honestly there's no circumstance that I would ever, ever, ever use a shipping company for my horse but I understand not everybody owns these things, but even if I didn't, I wouldn't ship my horse anywhere.