The dormancy period of a peach tree starts when the tree loses its leaves in fall and it lasts until the growth starts again come spring. Every peach tree has this dormant stage, where it shows no signs of growth on the exterior. The first signs of a peach tree coming out of dormancy is when the flower beds start to swell. At this point there will still be no green tissue growing, but the swelling of the buds will indicate the time to start pruning peaches has arrived.