Garry,
Late January to early February would be my preference to see the winter scenery. There are some really nice places to stay in West Yellowstone, MT. Nice motels with attached restaurants. The tours will pick you up at your motel. The tours are not that expensive. There are several. My wife raised a flatlander, hates winter travel. She was with me on this trip and her only regret was we couldn't stay a couple more days to take all 3 of the major tours. Our day long tour in the snowcoach (a transformer really..it's tour bus in the summer) was $95 per person IIRC. That didn't include lunch. It was a full 9 hours long and the drivers are as much tour guides as drivers. We learned a lot on the tour! The snow coaches are comfortable.