Not so sure weather is that much of a factor. Russia is the original cold weather attack dog. Putin will move when he thinks the political weather is in his favor, IMO. The USA and NATO (neutered organization) will huff and puff and do nothing of substance. The UN will...well, do what the UN does. Cry.
Weather may or may not be nearly as much of a limiting factor as it was in the Second World War in Eastern Europe, but it does remain a less advantageous factor for a military campaign when it is not the prime Summer military campaigning season.
Putin also has to deal with the fact Russia has generally exhausted the supply of military age conscripts due to declining demographics. Consequently, he needs to keep the troop commitments modest and the casualties minimal. Adverse weather conditions quickly melt away divisions and brigades very quickly in day to day filed operations, especially in the absence of a troop replacement system. Putin needs to accomplish his aggressions with prolonged low intensity conflict and/or a very short and economical high intensity combat operation with minimal casualties. Adverse weather greatly increases the risks of prolonging a high intensity combat operation and incurring politically troublesome casualties in the process.