Freddy, you do want to be careful about what kind of wood you use for places that horses will be. Horse chew the wood when they are bored or just plain mean. Some kinds of wood are very dangerous to them. The splinters is one thing that can cause all sorts of trouble. Walnut wood is poisonous to horses.
When you get your barn plans, you might want to check at the Sawing and Drying forum at www.WoodWeb.com or in their knowledge base. It is common to build barns from green (not dried) wood since that is a lot cheaper. Plans for barns should take the fact that horse are involved into consideration. Building with green wood is somewhat different than building with dried wood since the wood moves and shrinks during drying.
Perhaps you could check at WoodWeb for someone with a sawmill near your area and start that way--with what wood you want and can get locally.