about the starting problem,it seems the battery and starter are fine. The problem is either ignition, or fuel, or engine compression. If you haven't changed spark plugs for 8 years, now it is time to do it. Cold temperature makes fuel hard to ignite and could cause engine to be flooded with unburned fuel.Your engine may also have low compression due to wear.
The squeaking noise is usually from loose alternator belt. Yes, cold weather make it worse.