I have two in the house, one is upstairs and one is downstairs. I have a two in the shop, one is in the office and the other is behind the counter. I have three in the barn, one extinguisher at each exit and one hung in the very middle. You should definitely get one or more for the barn! All that animal bedding and wood will burn quickly!
My insurance requires us to have several of them throughout the property. The firefighters came out and did an inspection and gave me tons of extra tips for how to best maintain fire safety. It was interesting, and they gave practical tips for fire prevention and how to lessen the impact if one is inevitable. Here they offer it as a free service won't even take donations for it. You might check if your community offers that as well. If they charged a fee it would be worth every penny to me.
We have 1 in the kitchen of the house and a larger one in the garage where chemicals and gas are. Just a tip, but if you have those sorts of things in a garage or out-building, keep them by a window or a door and keep the fire extinguisher on the other side of the building.
I think it's definitely a good idea to have an extinguisher for your barn. Maybe even two or three if your barn is large. That way, you'll always be able to get to an extinguisher quickly if a fire breaks out.
Businesses have to have a certain amount in accordance to the square feet of the building per fire code. I don't see how that would be a bad idea for the structures on a property that a family has. Maybe there are insurance discounts for this.