Just yankin' your chain. This morning would be a PERFECT freezing azz morning to see if the choke opens on startup.
What, exactly is it doing when it's cold? Is it chugging, belching black smoke, or...?? There may be something else of concern.
But from the description of it running perfectly fine after warm up tells me that it's likely in the choke system somehow. I believe that is an electric choke. So it seems that part is working.
I gave you the GM part numbers in case you needed to find one for your car and can either get the GM one or an aftermarket equivalent of that number so you know it should fit. Standard has one for the 305 2 or 4 bbl listed under part CPA141 for less than 20 bucks at O'reilly auto parts, and Echlin at Napa has one under CRB 24832 at twice the price, should you find you need one. Around $40 on ebay for an NOS one.