score:3
If you go to http://tripcheck.com, you can get the Oregon Department of Transportation's report on road conditions.
In particular, the little blue circles on the map indicate "snow zones"; you can click them for information on how much snow is on the road, etc. Also noted are chain requirements; it seems that all of them are marked "Carry chains regardless of conditions". There are links for information on Oregon's chain laws.
In particular, it appears that every route from Portland to Bend includes sections where it is mandatory to carry chains, including US 26, OR 22, US 20, and even the I-84 route suggested by Mark. So if you don't have chains, you can't go.
I agree that the I-84 route seems least likely to be snowy. But a better idea would be to check the conditions shortly before your trip. You can then evaluate which route is best, or if it is safe to go at all. (Do not underestimate this last part! If you are not comfortable with the road conditions you might encounter, it is much better to stay home. Once you are on your way, there's a condition that people call "get-there-itis" which may tend to pressure you to go on even if it's not safe.)
Upvote:5
If you've truly never driven on ice or snow before, my recommendation is: neither. A winding mountain road is not the place to be learning. The first time you try to stop, you will skid, the first time you take a corner, you will be going too fast, and it's much better to do so in a place where the worst that can happen is that a tow truck needs to pull your car out of the ditch.
My recommended route is to take I-84 to US-197 to US-97 to Bend. You cross the Cascades near sea level, so it's far less likely to have snow. It's about 45 minutes longer under normal conditions, but if US-26 and SR-22 are snowy, it could be considerably faster.