October is generally the month for engaging in transplanting (and other preparations in areas where the ground freezes) Japanese maple (Acer palmatum) as well as just about anything else. The thought is that it's easier for the plant to become accustomed to its new environment when it isn't actively growing and having to parcel out its life-sustaining activities in a number of ways (photosynthesizing, producing, respiring, stress-busting). Fall transplanted plants marshal resources specifically to survival while shutting down without the competing demands or priorities of budding, flowering, fruiting.
Winter sometimes may offer a less than ideal scenario of drying cold weather. But it also offers below-surface soil moisture and above-surface ice/snow cover which will melt and seep into the ground.
Some opt for a spring transplant, which can work. But such a timing for transplanting tends to be quite difficult for the newest plant on the block to become established when springs are rainy and windy and summers are dry and hot.