Yes, if it won't turnover fast enough then battery is marginal for cold weather starting.
If battery is able to crank engine then it could be a couple of things causing no start when cold.
When temp drops an engine needs more fuel to start, that's what the Choke plate on carbs was for, when closed more fuel would be sucked out of jets to richen fuel mix for starting.
Fuel injection can't use a Choke plate, no jets, so there is a temp sensor, used only by the computer, the ECT sensor, computer reads the temp when key is first turned on and then adds the extra fuel for starting cold, the colder it is the more fuel is added.
ECT sensor on 4.0l is just above thermostat housing on lower intake, there are 2 units there, the one with 1 wire is for the dash board temp gauge, it is a Sender, the 2 wire unit is the ECT sensor.
ECT sensors rarely fail, but not never.
If ECT sensor is not reporting colder temps then computer wouldn't know to increase fuel.
These sensors can be tested with volt or ohm meter.
Second reason could be ECT sensor is working fine and computer is adding the extra fuel needed, but with this extra fuel you also need a good hot spark or added fuel will drown the plugs.
4.0l used distributorless EDIS spark system, so only thing to check is plug gap and wires where they plug into coil.
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