Hi Rohan, You can take a train from Dehradun to Kathgodam then take a taxi or bus to Nainital. You can also take a bus to Nainital directly. Snowfall depends on the weather that day, we can only hope. You can read more about Nainital in the trips and guide attached below. Keep exploring!
You can take train or bus till kathgodam and take a bus or taxi to reach Nainital. It is tough to see the snow in the december because in Nainital Mid Jan is best time to see the snow. However if you are lucky you can witness in the December too