It's what makes attribution studies so difficult. Many weather events were likely to happen on their own, but are exacerbated by climate change.
Winter is going to happen regardless of how the climate changes, the question is how much better/worse is it because of those changes. A lot of climate science is known unknowns. We know things are going to change but not necessarily how or to what magnitude. Some things are easier like average temps or TC strength. Others are more difficult.
But adding heat and therefore increasing the potential water vapor in the air could lead to larger areas of convection and more latent heating, which as you point out can have significant downstream knock on effects.