An easy starting engine will mask the inevitable decline in battery capacity over time, taking as little as 5% of new capacity, which is quickly replaced once engine started.
Cold weather hits you on two fronts though, slower cranking caused by thicker oil and less current available from battery due to its chemistry. Add in the fact during winter that car is started less frequently and your previously apparently fine battery gives up in disgust as you have found
A full re-charge will offer only temporary respite with such a battery as it's very much at the end of its downward spiral, retaining only a fraction of its original capacity.
