I have a 2011 mini cooper s with just 19k miles. This is the first winter I have had it. When i start it up when the motors cold it struggles to stay running and usually stalls if i don't feather the gas. I got a check engine light for "intake temp to low". So i put back on the stock air box. The check engine light has stayed off but did nothing to the cold start issue. (ignore the check light/light) damn led bulbs. lol

 

Maybe a cylinder issue, just a coincidence that it's cold out?

 

When mine did that it was diagnosed by Mini to be the carbon build up. After they cleaned it out it did the same thing. Second time they replaced the fuel injectors and spark plugs and it did the same thing. Third trip they replaced the high pressure fuel pump and haven't had the problem since.