Hello, we have just crossed the Georgian Military Highway. There are numerous tunnels en route which were being repaired as we drove up on the Kazbegi side, which implies that they are preparing it for winter. It is mostly scrubby potholed dirt road on this side, so not much fun in the ice and snow.
On the Tbilisi side there is a ski resort, and the road is mostly tarmac, so they must keep it clear for the skiiers to get to the resort.
It was 6 decrees C at 9 am last week (early September) when we camped in Kazbegi, so enjoy the weather in January!