If your battery is dieing, you likely have a parasitic drain or its failing. Cold weather really does a number on batteries.
me too I've been running 87 octane since day one with no issues other than a little carbon buildup. I live in south Texas so I am not sure if ambient temperature makes a difference.I run 20-50 petro oil and have no problem, even in sub-zero weather.
The OP doesn't state if the problem is slow cranking or just failure to start.
By the way, you're wasting money on higher octane fuel.
Higher octane does NOT mean the car will start or run better. High octane gasoline is widely misunderstood.
It's for high compression engines that are prone to detonation/pre-ignition, which was an issue with carburetors and old-style ignition systems. Modern technology normally incorporates knock sensor/computer engine management, which gets around the problems associated with octane requirements, unless the need for higher octane is stated in the owners' manual.
Our 2 liter four-bangers run just fine on 87 octane.