This is what worries me "Especially in colder weather".
Read the whole sentence. It says "Especially in colder weather, breathability is crucial for keeping your feet dry and warm." It's suggesting that breathability is especally important in cold weather not that Gore Tex only breathes in cold weather.
If you want to keep your feet dry then also make sure not to use cotton socks. Cotton just holds the moisture next to your skin while many synthetic materials will wick the moisture away. This is more important in cold weather because it can mean the difference between toasty feet and frost bite.