Very hard to start when cold (5 celcius or less)

well your battery might not like the cold,,, for starting,,, have you tried jimping it to see if it's hat?

as far as the poor warm up idle,  in my experience a bad idle air controller will do what your experiencing..

When you hit thegas during warm up:

The ECU thinks your going to drive and it kicks out of warm up mode... why does the ecu do this? well you'll have limited low speed throttle control if the IAC  is open and this could be dangerous.

possibly a battery in poor health would be a burden on the electrical system when cold... thus things that need a little extra voltage like the IAC might not function right...

dunno hope this helped

Have you checked your glow plugs?.... Kidding, I used to drive a diesel, anyway I second ZED_not_zee. Your first point makes me think weak battery or old spark plugs. If its your IAC I think those can be taken off and cleaned with carb and/or throttle body cleaner, the spring in them can get gunked up (correct me if I'm wrong anyone).

Battery voltage is fine and it doesnt matter if plugs are new or old (did the same with new plugs). The engine cranks very easily, its just that it feels like its missing air to do the job, hence why I have to quickly depress the throttle pedal a few times. I've been wanting to remove the IAC and clean it over summer but never had the time to do it. Had a quicky try last winter at some point but the 2 (or is it 3, cant remember) allen bolts are hard to reach with a ratchet or allen key because of the damn Y bracket at the back.... I was pissed when I saw that the previous owner had changed the clutch but didnt remove the bracket.

Hey vision, I experience the exact same thing as the weather gets colder, minus needing to press the throttle while cranking. My rpms start off around 1100, then floats around/drops a little, and eventually they jump to 1500 and it feels fine... Giving gas before the engine is smoothly idling at 1500 results in an rpm drop, as you described. 
I'll check my battery voltage soon but I don't think my battery is weak.

i had same issue i changed my plugs and it seemed to cure it. its bad cuz it makes you look like a took when your car takes for ever to start lol. best of luck

I've had some rough-start issues in the past as well, not exactly like yours but check this out:

http://www.canadagtir.com/forums/technical/misc-tech/anyone-have-rough-start-issues

BTW, since I posted this thread (ages ago), I've changed my fuel pump, fuel filter, plugs, plug wires, cap and rotor.

I had a shop try to clean out my IAC, it helped although didn't fully fix the issue. I also still have some slight idle problems, where once I drive around for a few blocks after start-up, then come to a stop light the engine will drop down to 1000 rpms and idle there (great), but once the car is REALLY warm, the engine will drop to ~1250 rpms at a stop light and idle there. If I slightly let the clutch out with the car in gear and my foot on the brake (IOW force the rpms down with load), the engine will idle at 1000 rpms again. Strange.

If you're starting your car and it hesitates to fire up, instead of pumping the gas pedal immediately try just lightly depressing the pedal down about 1/4 of the way and see if it starts any better. When I had my "problem" that's what I did and it seemed to help.

Last year when it was doing that, I've tried plug, wires and distributor from my other R, same crap happened. Pump was changed last summer for a walbro, fuel filter is newish.

Seems like my issue is exactly the same as yours, because the trick I use is exactly the same, press the pedal 1/4 - 1/2 way through a few times while cranking (too much pressure = doesnt start). I'm going to remove my iacv over the weekend to take it apart and clean in. Its most likely clogged with oil fumes as my intake piping has much of it on the walls, and the bov spits oil fumes under the hood too.

if you can check the ground going to the iac while your at it you'll rule out one more issue.   only way I could figure to check the signal to the IAC is to have a meter on the harness while starting the car... just to make sure it's getting proper signal...  this might be a little more involved than checking the ground but if your ripping it all apart anyhow...

In my mazda(i know unrelated, but trying to help)

The Rough idle and issues related to the engine '' starving for air'' came from the MAF.

im waiting for my consult connector to repair my consult cable, so i'll be able to diagnose better with a laptop connected and recording every sensor reading

Here's a video I took after work today

http://www.youtube.com/watch?v=7p6gwF6qWkw