I'm going to give you a cautious "yes". The reason I'm being cautious is that it depends partly on a hypothesis that is, and has always been, controversial. If it's correct, then absolutely, this scenario is possible. If it's wrong . . . well, perhaps the following reasoning is incorrect.
Have you ever read about the Snowball Earth theory? It's actually pretty fascinating. It posits that, within the last 650 million years, the Earth has frozen over at least once to an extent never before seen . . . except in a previous such incident. The theory attributes this period to any one of a number of events, including a large supervolcano erupting, changes in the Earth's orbit, or an enormous change in levels of greenhouse gases in the atmosphere.
The point is, at one or more times in Earth's past, it may have been a giant ball of ice and snow. Now, in order to cool the Earth, you would want to have extremely low levels of carbon dioxide. And I mean extremely low. Forget the current 1% or so; I mean a large reduction of CO2 and CH4 levels. What fills that gap? I would assume that oxygen and nitrogen would continue to dominate; given that they currently account for nearly all of Earth's atmosphere, it would be very difficult to reduce them to negligible amounts. Also, you would have to find something to replace them, which would be tough. In short, oxygen most likely existed during these snowball periods.
As for life. . . Less CO2 means that plants and other photosynthetic organisms have it tough; this also means that nearly everyone else has it tough, too. As the Wikipedia page notes,
Detractors argue that this kind of glaciation would have made life extinct entirely. However, microfossils such as stromatolites and oncolites prove that, in shallow marine environments at least, life did not suffer any perturbation. Instead life developed a trophic complexity and survived the cold period unscathed.
The page goes on to describe various extremophiles that would have survived. But I would think this expedition should be okay. They could grow their own plants and use them for food, get power from the Sun, and live as good a life as you can live when you're living on a giant snowball.
There's another bit of evidence staring you (and me) right in the face: Jupiter's moon, Europa. Yes, it's a moon, not a planet, but I can imagine that a scaled-up version wouldn't change to much at the fundamental level. Also, we know it exists and is frozen over (and has been for quite some time), so I think I can use it as a decent example.
Europa has a surface of ice (yes, from water) that may be many km deep. It seems to cover the moon's entire surface (it's average surface temperature, by the way, is about 50 K - way colder than you're looking for - but I'll ignore that for now). Below may lie an ocean, which has fascinated people ever since the idea was proposed. Its atmosphere, too, contains a lot of oxygen. Sure, it's a thin atmosphere, but at least it's something. The conditions aren't too good for life to develop on the surface, but a well-prepared team of explorers should be hardy enough to survive.