The thing is, having more room in the shoe increases the blood circulation ... that's the trick! Or rather, it doesn't cut it off.
Was your wool sock (or liner sock) a knee-high? I find if my calves are warm, my feet are warmer. My wool socks come right to my knees.
I rode the Golden Triangle last year ... a tour in May in the Rocky Mountains ... and I watched one particular woman.
Day 1: despite the fact that it was cold and rainy, with a bit of snow and hail thrown in for good measure, she had on knickers which came just below her knees, and tiny cycling socks, small roadie cycling shoes, and little shoe covers. I wouldn't even call them booties. She came into every rest stop complaining bitterly about how cold her feet were.
Day 2: similar weather, same gear. She'd past the point of complaining to everyone around. At every rest stop she sat huddled in the grass with her arms around her feet, moaning in pain.
Day 3: similar weather ... and she must have hit a bicycle shop! She had full length tights, and I couldn't tell what kind of socks or shoes because she had heavy neoprene booties. And she was all smiles again. Yes, the booties probably made a difference, but so did the full length tights.
And when it gets down to the temps we're talking about, I like full length tights (often with sweatpants over them) with knee-length wool socks underneath ... all with the goal of keeping my legs warm ... warming the blood before it enters the foot. Sort of like the principles of the duck.