John Rose is right. Make sure your battery is up to house temperature before charging it. Also for safety while charging a battery, just make sure you are present, you don't charge it overnight and you use Rad's charger. Rad's batteries are pretty safe as they use quality cells, have a decent Battery Management System (BMS) and they are CE certified (European Union standards). I think they are working on getting CSA and UL listed too.
Your ebike battery will lose capacity in the cold. However, if your rides are relatively short it shouldn't be a problem as most of us ride less than 10 Km when we ride and that's not an issue with an ebike. When you stop somewhere take the battery inside with you so it has a chance to warm up a bit. It's what I do although I don't do it for the sake of the battery. I do it as they are ridiculously easy to steal if left on the bike.