"And, once fully grown, the damage done by jumping. I love drafts, but it worries me that I would hurt them if I ever wanted to jump over 3'. "
Just saying my draft can walk over a 3' jump with no problems!
He thinks that large, blue drums are ground poles!
I got my Percheron as a 18hh, untouched, 3 year old. He is now a 19hh, 2100 pound, 5 year old. It took me a LONG time to get him to trust, listen, behave and understand that while I was smaller than him, I AM THE BOSS. When a horse is big, they know it and they know how to use their size! Make sure that if you do this, that you have a trainer, that is familiar with drafts. While they are a horse, their size makes many things different. It does take a bit of a search to find a lead rope that is long enough (I made mine), a halter that is big enough and the list goes on. There are great draft horse supply stores, use them, it's the only way that you know that stuff will fit!
I now ride my horse daily and he's great. A draft horse isn't done growing until age 5-7, so riding them early is not advised. Most people think that just because they are big, they can be mounted and the rider can be bigger. This is not true. Take the time, ground work, drive, etc, but I would wait until at least 4 years to back a draft. Others may disagree, this is just my opinion.
As far as the vet, the cost is the same as a "regular" horse. Farrier, I have one that specializes in drafts and he is about the same. My guy is barefoot and gets trimmed every 6 weeks at a cost of $60.00 per trim. A "regular" horse trim is $50.00, so not much more. WORTH IT! I love my farrier!
It does cost me more for wormer, supplements, etc. My horse needs twice the amount of almost everything for this type of stuff. Though, drafts are more affected by some medications, so you need to make sure that your vet understands this.
The big guys are worth it, in my humble opinion, once you go draft you never go back! Keep in mind though that like non draft horses, they are all different so if you want one that moves with a bit more style, try them out. A Belgian is different than a Shire, which is different from a Percheron and so on. It's a BIG (pun intended) investment, pick the one that will work for you.