Real bears are nothing like Winnie-the-Pooh. They're not even like the Berenstain Bears. They're huge and angry and basically real-life monsters. With this in mind, we advise you not to mess with them. Even if you're on a snowmobile, feeling like a henchman in a Bond movie, don't mess with bears. Just to reiterate this extremely sound advice: Don't mess with giant bears.
For a great example of why you shouldn't do that, behold the video above. These snowmobile-riders are trying to chase a bear away from their fishing camp in Paramushir in Russia's Kuril Islands. They follow the bear, pushing it further out it (through some honestly stunning white scenery) and circling back on it. Then one rider gets too close and the bear takes a huge swipe at him. If it had landed, this would've been quite a different video.
The YouTube commenters were pretty pro-bear here. "This is one of those times you cheer for the animal kingdom!!" says one of the tamer messages. However you feel about the wisdom of chasing a bear on a snowmobile through a snowscape, we can probably all agree this turned out about as well it could've. There's a pretty cool video, and everyone's head is still attached to their body.
One more time: Please don't mess with bears.