If you crank it all the way the power steering pump will make a light humming noise that you can feel in the steering column, but that's perfectly normal on every car and doesn't sound like what you're experiencing. So it doesn't make this noise at all if it's say, 60 deg outside? Has it repeated itself throughout seasons, or did it start this winter? Just trying to make sure you don't draw a causal relationship between cold and the noise prematurely.
E88 FBO N54 Alpinweiss/Coral Red/Meisterschaft Race/Berk Resonated/Macht Schnell 3"/ER CP/Synapse/VRSF FMIC/FFTEC LPFP/HFS-4 DO Stainless Lines/BMS DCI/BMS Thermostat Delete/Rob Beck PCV Valve + Cap/BMS OCC/PTF E50/ST Coilovers/M3 Front Control Arms + Tension Rods/M3 Subframe Bushings/M3 FSB/DINAN Camber Plates/Apex ARC-8/Project Kics/Macht Schnell Studs/VAC Hubs/Rogue Transmission Mounts/Alpina TCU Flash/Icarbon/Kerscher/BMW Performance