Broccoli does like it cold. My spring broccoli I start indoors under lights and then move the plants out into the garden at least a month ahead of my average last frost date. It goes through snow and freezes quite well once hardened. I have little broccoli plants potted up, going in and out starting to harden off right now. They are sitting on the floor next to me as I type, keeping me company
. They will go back out in a couple hours when it warms up a little. They will go in the ground pretty much as soon as the ground can be worked.
But like applestar, I have never been able to work out how to do fall broccoli; it seems to need to be started pretty early while all the summer stuff is still going strong. HOWEVER, I have direct seeded broccoli in the ground early Oct to overwinter. The little plants sprout and get started and then go dormant, then start growing again late winter. The Sept 25 date may refer to that. I did that with no protection for them at all. One year when we had a milder winter, it worked beautifully and I had a wonderful early spring broccoli crop. The next year the winter was a lot harsher and the broccoli died (though spinach that was planted the same time made it through and did well- spinach is amazing that way). [Fortunately I did not plant anything this past Oct, I can't imagine it would have made it through the winter we have had.] But that was without protection. If you were willing to give it just a bit of protection like a polytunnel, I bet it would make it through a lot of winters.