Yup. Traditionally, butter was made with slightly soured cream - that's why buttermilk was sour. In fact, it was intentionally cultured to acheive that.
But, it's not to many modern tastes. Try as I might, I can not get a handle on sour butter. My dh won't touch it with a ten foot pole - in fact, if I use it for cooking, he leaves the house from the smell. The smell/flavor are definately less prominant when the butter is cold. I'd use it just for spreading on bread and things. Or maybe for things that involve other sour flavors - basting fish, where you'll be squeezing on some lemon then, etc.