Want to drive to Yellowstone in February; any tips?

Hi,
I'm from the SF Bay Area, with not much experience driving in very cold weather. So this may not be too wise, but my husband and I would like to drive to Yellowstone in February, to go see the wolves in Lamar Valley.

The route there will be mostly on Interstates, but I have heard that the temperatures might go as low as -20 F or maybe even lower.

We have a 2005 Prius and it's doing great. My concern is not so much the mileage, but whether it would be advisable to drive it vs. some other car (one that can stay warm even when not moving) when facing extreme winter conditions. Also, whether we should consider switching to all-weather or snow tires at some point.

Would anybody have any advice?

Thank you,
-Cold Weather Wimp