The craziest weather I can remember in Georgia is in the summers. They're kind of during monsoon season, you'll get these crazy rainstorms and they, a lot of times, like the city and like Rustavi and Tbilisi, parts of the city will start flooding just because like the drainage system isn't very good. And so you'll have like crazy lightning storms and thunder and it'll be raining a lot but then everything around you will start flooding.
So Tbilisi can get pretty cold depending on the time of year. When I was there, there wasn't a lot of snow but there can be a lot of snow. I would definitely recommend getting a huge jacket because when I was there, I was in Varkotili at the time and the wind was insane. Like, it can get so windy depending on where you are in the city. It seriously would blow our door open in the middle of the night and blow out our heater and so it was so cold and we were just like always wearing big, big coats.