cold weather stall

i have a 74 bug that's been restored inside and out. In really cold weather when i first crank the car in the morning, the idle is really high and loud and then it idles down to where it stops running. When i first accelerate, there is a bit of a hesitation as if gas isn't getting to the carb. Also, whenever i step on the brakes to slow or stop, the car will usually stop running. These problems usually happen within the first few miles of driving in really cold weather. I've had the carb overhauled, choke adjusted, a new heater element put on the choke and none of these have helped. Also, whenever i turn on the heater i smell exhaust fumes. I have a header style exhaust system.I don't know if that would have anything to do with it..But any suggestions would greatly be appreciated. Thanks.