It's possible to use either here, but "will be" is probably the better choice.
"This winter will be much colder" is a prediction. "This winter is going to be much colder" implies that the winter is very near, or even already started, and already it's very cold. "Going to" is usually used when the process has already started or is very close to starting.
In many cases, including this one, you could use either. Sometimes it's hard to tell.