From a mechanical point of view, if the engine would be at the same settings as when warm, the cold engine would have lower rpm (and stall/not start), so: yes.
But cars nowadays have a "cold start device" that will raise the rpm after a cold start until the engine is warm. This will offset the "naturally lowered" cold start rpm and can range from not completely compensating the lowered rpm to overcompensating depending on the type of cold start device and on the programming of the cold start electronics. So in that respect the answer is: no.
The behaviour you observe with a recent car like yours where the engine behaviour is controlled electronically has little to do with what you can expect from a engine mechanical point of view and all to do with how the engineers who developed the machine decided it should behave in a cold start with low ambient temperature.
The first stage of this cold start procedure are the first few seconds until the engine is warm enough not to stall (that's what in ancient times the choke was for, or for diesel engines the "earlier injection"* or the "raised minimum rpm" cable). For gasoline cars, you have then a longer period where the minimum rpm is raised (over the warm "proper" idling which you quote for your car at 600 - 700 rpm) because the convertor and λ probe need to be warmed up asap so they start to work, even if you do not drive but idle. The minimum rpm you observe during this period is still not the proper idle rpm. It is an (electronically) raised rpm in order to make the engine warm up faster.
Whether this raised rpm is faster or slower with colder ambient temperature primarily depends on what the engine development specified how this raising should be programmed (e.g. whether the specification goes for an increased injected volume or for a fixed rpm. You could (should?) re-program it in another way.
Do I need to wait before driving the car?
If everything is as it should be, there should not be any need of waiting more than maybe few seconds (maybe 1 - 3, but 10 would be long even with my old diesel from the pre-electronic era which of late coughs a bit on one cylinder when it is cold).
If there's a bit of trouble with the engine, I'd wait to be sure it doesn't stall at the next crossing when you step off the gas.
This sounds like a description of the second stage (which in fact may be several stages) of the warming up:
I generally wait until it goes down from 1600 to about 1000 RPM before driving, which generally takes maybe half a minute or so
Warming up by idling (the 600 rpm idling) is not only bad for the environment, but also for the engine. It is generally recommended to warm up the engine at moderate rpm and power, i.e. by driving in a civilized fashion.
My guess is that the raised rpm (over the warm engine idling rpm) is just the cold start device making sure the car is warming up fast even though you refuse to start driving.
In other words, the engineer designing your engine knew that people would leave the cold engine idling and had an increased rpm programmed for the warm up phase of the engine for one or two purposes
- environmental norms have to be met which nowadays include the emission after cold start, and
- this is also better for the engine.
* The mechanical "earlier injection" for diesel engines does not raise the rpm. As the injection is nowadays electronically controlled it would easily be possible to adjust the injection likewise. I do not know whether there exist engines where this is done without raising the minimum rpm. So I cannot even answer that the minumum rpm immediately after a cold start is always higher.
