1999 Acura Integra Car hates the cold!

I live in Utah and it seems every winter my car progressively runs worse when its cold outside (near freezing and below). Symptoms include rough idling, heater doesn't work, car will warm up then when driving cools back down, shifts and runs harder. I can tell it just doesn't like the cold. Now that it's warmer it runs completely fine and sounds great! What would cause my car to do this? Could it be fixed or does that just happen with age?