When is a good time to fertilize trees to help during cold winter?
Part of the question depends on what type of trees you're talking about. Shade/landscape trees don't require much in the way of fertilizing; in fact, fertilizing, especially late in the year, is a very bad idea. This article will tell you more: https://www.gardeningknowhow.com/ornamental/trees/tgen/dry-brittle-tree-branches.htm
Here are a couple of articles that might give you some more ideas for winter preparation: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/fall-gardening-tips.htm