The chainsaw oiler is usually just clogged.
Probably.
Nine times out of ten, the oil port is plugged with sawdust and pitch. A quick clean with a wire (or a compressed air blast) gets it dripping again.
If that doesn’t do it, check the tank—air in the line can stop the flow. Fill it up, let it sit, then run the saw at idle for a few seconds. Still dry? The pump might be worn or broken, but don’t jump to that until you’ve ruled out the easy stuff.
Also: don’t use bar oil that’s thicker than the manual says. Cold weather turns heavy oil into molasses.
Save the pump rebuild for the last resort. Clean the port first.