According to Roads Department of the Ministry of Regional Development and Infrastructure of Georgia, there are no restrictions on entry to Tbilisi

Due to adverse weather, in particular, glaze ice, wind and limited visibility, and also for the purpose of traffic safety, movement at Tbilisi Bypass (detour) road has been restricted for 3 hours for all types of transport. At this stage, traffic is restricted only for trailers and semi-trailers. Tbilisi bypass road starts from Zahesi bridge and joins Rustavi-Red bridge road.  It should be noted that this route is mostly used by transit vehicles.