This trip was completed from late December 2016 to January 2017, starting in Ulaanbaatar, Mongolia, with a stop in Irkutsk and Lake Baikal, and ending in Moscow, Russia.
The biggest item to book, logistics wise, is the train ticket. I found the time-table and articles by the Man in Seat 61 quite helpful (link to his article about how to plan and book a journey here). We took a Chinese operated train from Ulaanbaatar to Irkutsk, and, after a week celebrating the new year in Irkutsk (with clementines!) and Lake Baikal, hopped on the Russian tourist-grade express train “Vostok” for Moscow. We purchased the tickets from local travel agencies (yup, some research on TripAdvisor should be helpful to find the latest reviews) and arranged the tickets to be picked up at the front desk when we checked in. For the ticket to Irkutsk, we used Solid-Ways/Train to Mongolia (website link here) and paid in advance online. For the ticket to Moscow, we used Baikal Explorer (website link here) and paid for the tickets when we met with our guide (we also booked a trip with them for Lake Baikal).
The train ride was very clean, warm and nice in general. Unlike the bustling summer rides, winter was considered to be a “low-season” and we were the only passenger in the first class and were able to have all the solitude that we wanted from the one-week train ride. I kept tracking the temperature outside on my cellphone (AT&T’s local partners did lose coverage at some point in Siberia), and with the temperature at -30-40 C outside, the internal temperature was close to probably 20C and the only place we’d see signs of the cold inside the train was in between the cars. Even though there was cold water in our compartment, we talked to a conductor (some Russian language would really pay off for the off-season) and paid the equivalence of 1-2 dollars everyday for a steamy hot shower in the crew’s section. The dining car was well run and provided decent food (my favorite was the good old borscht and tea with milk).
The highlight of this trip, in addition to the experience of the train ride itself, was the frozen Lake Baikal and traditional Russian sauna on the Olkhon island. It was also a very pleasant break in the middle of the one-week long train ride.