The simple answer is, "Yes." Your mini-pond does rest during winter. That doesn't mean it isn't active - it is active, but at a slower pace. Some plants die, others go dormant. Water becomes denser, holding its cards near its chilly chest. Organic matter, those leaves which fell into the pond last fall, along with dead aquatic plant life on the bottom, slowly decomposes. Water holds the maximum amount of oxygen at these cold temperatures as long as it contacts the atmosphere.
Fish don't hibernate, but they don't move around a lot, either. Yes, they will be active from time to time, but not typically in rapid movement. They'll feed, but most fish in cold water need at least 24-36 hours to digest their food. Because of that fact, they don't feed quite as often.
It's also wise to be thoughtful about managing your aeration strategy. If you move too much dense, warm water to the surface, you run the risk of over-chilling it, much to the dismay of your fish. Consider moving your diffuser to shallow water if you want to aerate all winter. But, it may be the best idea to shut down the system for winter and start it again as water temperatures begin to rise next spring.
Remember this: think about the physical properties of your water, the plant life under water last fall, organic matter that made its way into the pond, and the fish community which resides beneath the surface. The more you can empathize with the entire system, the more you can understand what happens. The more you understand, the better decisions you can make.