1988 Dodge Aries K

I have that named model, mileage about 105440 miles.
I bought the car used back in June this year, and gave me no problems through the summer. Now, all of a sudden, because of it getting cold, when I start the car to idle in the morning, it dies immediately after I start it. Now, during the day, when I start it, or after I have driven it for a little while, it works better. While I'm driving it in the morning, it seems to jump forwards as if something's cranking wrong or something, dunno how to describe it. Only recently changed the oil and put new coolant-antifreeze in. What do you think? Plus, is the problem something I can fix myself, or do I have to bring it to a mechanic? I would prefer the earlier option, but, you know.