I live in Wisconsin and I am building a 32x40x10 pole barn. The plans I have call for 4x4 posts. Is this pole big enough or do I need to go with 6x6. The barn is just for shelter for some steers and a couple of horses.

If this is a set of engineered plans you can go bigger but not smaller. Double check with whoever issues building permits in your area to see what their cpodes call for,

Talk to these people. http://www.graberpost.com/
They have been selling and building pole buildings for almost 40 years. They sell over 100 million dollars worth of buildings every year. They have dealers in Wisconsin.

I have at least used 4X6 posts because steers and horses have the tendency to lean against things,rub,push,etc.

I have even seen the 4X6's break (within a week of installation), due to this, I would say go with the 6X6 ,what could the harm be?A few more bucks verses replacement of the post?