Then you were probably dressed too warm.
The strategy is to be slightly underdressed, then make up for it with the heat you generate when pedaling.
When you first step outside your first reaction should be, "Damn, I need another layer". Ignore this. Hop on your bike and ride. If after two or three miles you're still cold, then circle back for another layer. (Or pedal harder.)
If you step outside and feel perfectly comfortable, go back inside and shed a layer.
No matter how may times I post this advice, I still have to re-learn it every year myself. It's just a knee-jerk reaction to want to be warm when you first step outside. That will always get you soaked in sweat, which leads to getting chilled, and if it's cold enough, to hypothermia.
In all, it's a balancing act. The goal is to balance the heat you generate against the heat you lose. You need to plan the heat loss. You can't lose heat if you're dressed too warm.
+1. People at work are surprised in the morning when it's 39F and I walk into the building wearing shorts. I explain that I'm cold for the first five minutes, then just right for a little while, then too warm by the time I get there. For me around that temp, it's generally shorts, t-shirt, a lightweight nylon shell, and winter gloves (because that is cold enough to make my fingers hurt by the time I get to work).
Jim S.