Cold Day starting problems.

Starter, starter ground/power wires, plugs, disty, cap/rotor are a few very basic things to check. Even if it doesn't fix the problem, it is a good idea to replace them once in a while. My car occasionally does this, mainly only when sitting a few days.

check your cold start injector.

Run a couple of bottles of Fuel Injector cleaner through it. It might help if the cold start is partially plugged or you have an injector leaking down pressure.

I had this problem and I replaced my starter and it works great now, no problems starting up ever.

I had the same problem, I cleaned the connector of the start injector time switch and I seen that connectors "STA" and "STJ" stays releases and did not engage correctly, I have also changed the Star injector time switch and now it starts very well.
Look at here:
http://www.cygnusx1.net/supra/library/TSRM_MKII/fi/FI_071.html
(Excuse me for my English is not really good)

I have the same problem. Although I have try any of the idea from the above. In my case I notice the fuel pressure drop after the engine is cut off for awhile. Anyone has experience in this yet? Please share some info.
thanks!