Cold Starting Problems

[chevychic]

Now that the weather is considerably colder, I'm having some problems starting my truck. It starts fine and I need to give it a little gas after I first start it, but I can't leave it to let it warm up. I have to babysit for at least 5 minutes otherwise it'll die. I'm not a very patient person and sitting in a cold truck for 5 minutes+ is not something I want to do every morning.
It'll idle just fine for a minute or so but then it starts idling rough until it dies or I run outside and give it gas. Then it'll happen again a couple of minutes later. I don't have a garage at my new house so it sits outside all night.

Also if I get too impatient and don't wait at LEAST 5 - 10 minutes (closer to 10) for it to warm up, it'll die after about 5 minutes of driving. It starts right back up and will be fine the rest of the day.

This only happens in the morning and after it's warmed up from driving for about 20 minutes I have no problems the rest of the day.

I'm not sure when this truck had it's last tune-up so that's on my to do list soon.

What could be causing this?