TRANSMISSION SHIFTING IN COLD WHETHER

Vehicle Information: Year: 1981; Engine (size, modifications): 4.5L; Total Mileage: 120000; Transmission type: Manual;

I have a 1981 Porsche 928s with a 5 speed transmission. The transmission is original and it has been recently rebuilt. The shifting problem I was having with the syncros is now solved and I am able to shift gears without a problem. The only problem that I am having is in the morning since NY has very cold winters. If I leave the car in gear the day before whether it is reverse, 1st, second or any gear, in the following day I cannot remove it out and put it in neutral until the transmission oil warms up, also if I leave it in neutral I cannot put it in gear. I know I should let the car warm up all the time but if I am in a hurry. I think it doesnt make sense, if thats the way it is. Is there anything I can do to make it better? What kind of oil should I have in there, and is there better oil I can use that withstands colder temperatures? Can I do anything to the transmission to make it better in the winter?