If you increase your running speed on a treadmill your outdoor speed will improve too. However if you are running a 24 minute 5k indoors, don't expect to run that outdoors as well, regardless of the gradient etc. Running outdoors includes the wind, varied running surfaces, more balance work etc so you just can't replicate that inside.
Honestly running outdoors in winter is not that bad, especially if you're doing shorter distances. Get yourself layered up, get some gloves etc and just get going, you warm up quickly once you're outside.