Question about Goal Zero Yeti 500X

No. It's not IP65 protected or anything like that. Moisture and certain cold temperatures don't do much for a short time. But a battery is usually not built for that either. There are special batteries for extreme applications. My Yeti 500 lives in the bike and does its job perfectly

For rain and snow I don't know, I store it in the cellar. But I don't think so!
In the cold, the battery loses power if it's not used, so you need to recharge it regularly. Once a month.