Anyone help me out?

hi guys

good to meeting you guys here, i am new, and also I know nothing about car. Last year I bought a 98' Nissan Altima, it runs well at the first several month. As the winter come, one day when i start the car and put in gear, the car just give a shake and the engine stall. At the beginning i thought it is occasional. But as the weather become cold and cold the problem became more and more pronounced.
then I found that my car need some time to warm up then it is ok. (if in extremly cold weather it will need up to 10 min to warm up)
I tried many garage even two nissan dealer one of the dealer did a transmission flushing for me and the other just lean the throttle head and intake but neither of them help.
when temperature goes up the problem alleviate somewhat, but the winter is on its way back I am so worried.
could anyone can tell what is the problem, is it transmisson? the nissan dealer told me to change the transmission wich will cost 3000 bucks i can hardly afford.

thank you