Your problem is that you are losing fuel pressure when fuel pump is off, not cold weather.
You notice it more when it is cold because it takes more fuel to start cold engine.
Ford has a safety feature that prevents fuel pump from running when engine is below 400rpms, so fuel doesn't pump out of broken fuel line or ??? after engine stalls.
When you first turn on the key the computer runs the fuel pump for 2 seconds, it "primes" the system, fuel pump won't come on again until engine starts, this 2 second run time adds about 10-15psi of pressure.
Your system needs 60 to 70psi of pressure to work well.
There is a check valve in the fuel pump, basically a flap that lets fuel flow out but not back in, and when you shut off the engine/pump the fuel pressure should hold above 50psi for many months because check valve is closed.
And when you start it again the fuel pump runs for 2 seconds and back up to 60-65psi for starting.
If this check valve fails or leaks, you will lose fuel pressure over a shorter time, say overnight.
Turning the key on and off 3 times makes for 30-45psi pressure which is enough to start engine and get RPMs up so pump is on full time and pressure is back up above 60psi.
Just to confirm this may be happening, there is a Schrader valve on the fuel rail, looks like a tire's air valve, same kind of cap on it, and same kind of pin in the center to release the pressure.
After starting engine shut it off, still cold, then test if there is pressure in the rail, be careful 60psi will give a good squirt of fuel.
Go ahead and drive it.
Now the next morning or after it sits for a few hours, before trying to start it, test for pressure again.
You can also get/rent a fuel pressure gauge
Unfortunately check valve is part of the fuel pump, so.....................
Just FYI, pumping the gas pedal on a fuel injected engine doesn't do anything, there is no accelerator pump to squirt extra gas in like a Carb had.
Computer knows the best way to start engine, don't bother with gas pedal.
Now if you hold the gas pedal down all the way and then try to start engine, it won't start.
Gas pedal down all the way at 0 RPMs tells computer to turn off fuel injectors, it is a method/computer program to clear a flooded engine.
If you have a manual transmission engine should be idling at 600-650rpm after engine is warmed up, 750-800rpm for automatic trans.
If idle really never gets below 1,000rpms then there is another issue not related to the fuel pressure problem