This is area specific and materials availability.
The industry standard for just about all TB farms I have been on is 16’ oak boards nailed on locust, (the best), these days 6X6 pressure treated which are readily available and there is no need to angle cut the tops for water run-off to avoid rotting.
IMO and others 4X4s are not stout enough and provide less nailing surface. But I have seen a number of “hobby” farms that use them. Like some of my friends who seem to have to replace broken ones far more than 6X6. Really depends on the horses and number of behind them.
Some farms use large round post. But these offer a very small nailing area. Your post layout has to be pretty darn exacting. Less nailing surface can and does lead to the boards warping.
Half rounds are popular also.
IMO and others all nailed wood fencing the post are set with 8’ spacing. Which is why 16’ oak fence board are the standard length. The boards are nailed up with staggered board lengths. With a 3 board, the first top board is 16’, middle board is 8’, bottom board, 16’. The next course 16’, middle 16’ bottom 8’. After this all the boards are 16’. So there are not 3 boards with their ends all “butted” ending on one post. Gives superior shear strength, if a post should get broken the spanning fence boards will hold it up. The boards are less likely to warp.
DO NOT use or be talked into using Hemlock boards for horses.
This is a link to our fencing in SE PA. Sorry for using Photo bucket, Hate the site, slow and too much junk. Any time I use it or check out others links I get plagued with emails EVERY day from them.
http://s1136.photobucket.com/user/gumtreestables/library/Horse%20Fencing%20Oak%20Slip%20board%20and%20Oak%20nailed?sort=3&page=1