There's the electric pump, its relay and the possibility of ice in the
fuel line or dirt and ice in the fuel filter. That's the choice IF
there's no fuel to the engine.
Of course, there's also the engine's cold start system which adds some
fuel to the intake specifically to get the motor started.
So how does one find out which of these possibilities is the culprit?
If it were my car, I'd loosen, not open, the fuel line to the engine and
briefly crank it with the starter. If there's a significant fuel leak
then there's fuel TO the engine and the cold start system ought to be
checked. But if there's no fuel leak then the fuel pump, fuel pump relay
or ice in the fuel line are the choices. If you hear the electric pump
run very briefly when switching the key ON then it's probably OK, if
not, the pump or its relay are suspect. If you do hear the pump but
there's no fuel you must consider the possibility of ice in the fuel
line and / or dirt and ice in the fuel filter.
Others here can tell you how to "jump" the relay to test the relay and pump.
The cold start system varies somewhat by engine. Basically there's a
temperature sensor, a time-temperature relay and an electric fuel valve
on the intake manifold. The cold start system won't work if any of the
three is defective or disconnected.
Hope this helps you get it running.