Not sure about anywhere else, but in Texas broccoli, cauliflower, spinach, and lettuce are fall/winter crops. I have never been able to start them outside either--always have to start them inside.
I've had great success growing spinach, lettuce, kale, cabbage and Swiss chard from seed outside, but never broccoli or cauliflower. Actually, a couple of freezing nights has done wonders to improve my leafy greens yield....so much so that I've had to feed nearly half of what I've grown to my chickens, which they certainly don't complain about. Oh...and beets and carrots too.