Lot’s of good comments here.
I used to prune “when the knife was sharp”. We still do some, for labor cosidrrations. But it’s best to prune peaches in warmer weather during the growing season.
Here’s a peach tree we pruned a few days ago.
Here’s one we pruned back to nothing a month ago.
We go through and rip out those upright shoots about this time. We don’t head them, we rip them out.
The caveat is that if it’s varieties which tend to produce a lot of blind wood, like Earlystar, we might head some back.
Honestly I can tear off an amazing amount of wood without pruners. Green wood is easy, but if you are agreesive, you can even tear off year old wood. It makes an ugly wound, but there is no downside to being rough with vigorous peach trees during the growing season. To put it bluntly, don’t pussy foot around. You can’t hardly hurt a vigorous peach tree during the growing season.
Vigorous peach trees are more weed than tree.