It's not clear which road notice you saw. Many forest and back roads are closed during the winter due to heavy snow. December can be a very iffy time to be crossing mountain passes. The biggest problem you might face on your trip (unless you come up 101 and the Oregon Coast) will be the Siskiyous between Yreka, CA and Ashland, OR. The I-5 around the Shasta Lakes area can also be nasty when it's foggy or icy.
You should forget seeing Crater Lake in December. It's a major detour, the lodge is closed for the winter and if the weather is poor, you might not even see the lake.
Multnomah Falls and the Columbia Gorge would be a good day-trip out of Portland (if the gorge isn't an icy wind tunnel at the time). The road to Mt. St. Helens will also be snowy and the Johnston Ridge Observatory is closed for the winter.
In short, not a great time for travel in mountainous areas. Lots for kids to see and do, however, along the way. Just stay off forest roads and any that indicate seasonally closed. We have a few fatalities every year by people who ignore such warnings.