Your cold start injector may not be working. Either the injector is
clogged or may not be getting currents to open. It gets current from
thermotime switch. This is what I would check first.

Cold start system not working. Temperature sensor, cold start valve and
time-temperature relay. If any of these fail your car's problem results.
First check connections starting at the cold start injector and trace
back. If nothing found amiss my $ would be on the time-temp relay.

The reason the engine coughs when you open the throttle is that the
mixture is too lean due to this problem.

Fuel pressure accumulator?

cp