Personally, I wouldn’t invest 270$ in a baterry. From my own experience even the cheapo’ batteries will do just fine.
Cold temperatures do not negatively affect your baterry. With lead-acid baterries the story is the same as with food. In cold weather, If properly charged, they will last longer. Lithium baterries are exact opposite.
Usually it’s usually already damaged baterry and the fact that the engine is harder to turn in the winter that finishes the baterry in cold weather.
If you use too small baterry, it’s also an issue. Even though you will use the same amount of energy on each start as from big baterry and then the engine recharges the battery right afterwards, strain differs greatly.
Let’s say that you use 40Ah baterry in a car that should have 70Ah baterry. Starting the engine will take just about 30A, but while the 70Ah baterry still has 40Ah left, 40Ah baterry has only 10Ah left. While you took less than 50% from the large baterry, you took 75% out of small baterry. Strain like this will degrade the plates and cause growth of crystals in the baterry.
Also, It’s really easy to just murder your baterry straight away. It usually won’t take more than three complete discharges (by leaving your lights on or running your laptop for too long) to kill the baterry. So if it happened to you, that you have completely discharged the baterry twice (or once and left it alone for a while), your baterry is likely to be seriously damaged or dead. Then, if you’re prone to do these discharges, there’s no point in buing high grade baterries, you’ll murder them anyways.
Short trips and frequent starts with only short time in between also kill your baterry. Although some people may recommend to you to switch the engine off on junctions. Even though such behaviour can save you gas, it won’t save your baterry.
Start/Stop systems also murder baterries. Special baterries are requred for cars like those. Also modern fuel saving cars can kill your baterry by improperly managing charging procedure, leaving your baterry dry.
So to prevent baterry damage, if you drive mostly short trips, no motorways etc. it’s perfectly ok to go and charge your baterry every now and then. If you can, charge it every day, it won’t hurt it. The one thing that kills lead-acid baterries is leaving them empty.
When it comes to diagnosing baterry, one way is to charge it, put it in the car, and start after 24h. If it starts it’s probably ok. Another problem could be the oil. If it’s worn out, it will be harder to turn the engine. You also may want to use some synthetic oil that starts with low number like 5W30 or 0W40 to have easier cold starts.