Have just come back from Churchill and would like to make the following comments about the experience.
Firstly I would not recommend using the train from Winnipeg to Churchill as although VIA Rail state it is a 36 hour journey with scheduled timings, the reality is that it is always late and much longer, the only question being how late and long. We departed 3.5 hours late and arrived there 8.5 hours late. With talking to the locals it is always at least 5 hours late!. It is actually a boring ride. The scenery is initially boreal forest, eventually changing to tiagra. After the first few miles of interest, both become very monotonous. The ride quality is terrible, partly because a trackbed across permafrost is inherently difficult to maintain, and partly because the owners for several years have skimped the maintenance anyway. It really rock and rolls. VIA use the track, they do not own it. As in all Canada, freight trains take precedence. The sleeping accommodation is cramped, probably no more so than other trains. The meals were pretty good and the staff friendly.
Churchill itself is not especially pretty or interesting. Access to the areas where Polar Bears may be seen is difficult, even if you rent wheels.
The two Tundra Buggy companies have an effective monopoly on access to the main area by the coast that is accessible, the old firing range. They do deliver sightings, frequently close up and good. But the ride quality is so bad on tracks across the tundra they are not allowed to maintain, that one has to question whether the experience is realistic for anyone with poor balance/ motion sickness: limited mobility: or frail/elderly. Presenting you with a long comprehensive legal disclaimer for you to sign is their opening greeting!! It is probable that the ride quality improves as it gets colder/freezing, which was not the case for us 20 - 24 October 2007. The frozen ground is harder, the water crossings freeze and smoothen, and snow is windswept into all dips and holes, then compressed, smoothing out the ride.

The dog sledging was informative and enjoyable. Without snow they used a wheeled vehicle, but one could still see the dogs work. The explanations about breeding, training and the racing of the team were very good.

The quality of hotel accommodation seems good. You need to book well in advance Most are bed only, but there are good independent cafes, so finding meals should present no difficulty.

Most people visiting Churchill to see polar bears do so as groups through a tour operator.

The air service seems excellent. There is a daily scheduled by Calm Air, with most tourists in groups using charter flights.

If doing the trip again would fly both ways and only go for the maximum of two nights.