Will using either to try and start the engine in cold weather cause any problems

Ether is not great to use aon an engine. It drys the cylinder walls so there is no lub to them on start up which after a period of time causes other problems. Plus it's downright dangerous to use. As you can blow the valve covers up oil pan etc. Have the car scanned for codes and check the coolant temp switch and fuel pressure. This car should start in coldweather especially with f.I. Someone has missed soemthing on the diagnosis.