2002 BMW 325 Transmission vs gear assembly

Transmission problem
2002 BMW 325 6 cyl All Wheel Drive Manual 90k miles

I have a 2002 bmw 325xi. For more than a year I have had trouble shifting gears when it is cold outside (<50'f). The gear shifter, while in neutral will pull hard to the right and sit over by 5th gear. Then to shift gears I have to pull it back to center to find third. It is also getting increasingly rough to shift - catching on something left sided when going into 1st. Once in gear the acceleration is phenomenal. I've been told that it is the transmission, but I think it may be the gear shift assembly. Hmmm?