Hello, Tim!
It's not so much that the Prius "benefits from battery power" during sustained driving. The Prius infrequently moves under battery power alone, regardless of trip length. A major benefit of the Prius' hybrid system is a small (1.5L) ICE (internal combustion engine) that runs efficiently at a variety of speeds, despite a car of almost 3000 lbs. Now, if that ICE was the only source of propulsion, then the car would be woefully underpowered. So the electric motor provides immediate and significant low-end torque for short bursts of acceleration when needed.
In addition, after a short warmup period, the Prius shuts the ICE down completely when not needed for propulsion -- coasting, braking, or idling. The warmup period, as you might guess, is lengthened in cold weather, and the ICE will run to keep itself warm. Running the cabin heat will lengthen the warmup even more and draw heat, causing the ICE to light even if not needed for propulsion. All of this costs fuel economy.
Short trips hurt MPG in all cars. The effect is probably magnified in the Prius because of this warmup period. For the first five minutes of driving with a cold ICE, results of 20-30 MPG are not uncommon, even in warm weather. 40-50 MPG for the next five minutes can be expected in typical conditions, though it will be lower if the heat is constantly run in cold weather at slow speeds. At highway speeds where the ICE runs continuously anyway, cabin heat has less effect.
Many of us have taken some simple and inexpensive steps to improve fuel economy in cold weather -- namely, an engine block heater and blocking the front grill. You might search here and on
PriusChat for more info on either of these if you want it. With those modifications, my first five minute MPG reading is usually at least 40, and can approach or even exceed 50 in warmer weather.
Good luck, and I hope that helps!