I can't recommend the San Juan in the Winter highly enough- it is the most beautiful place to be in the winter time. The permits are easy to get, there is no one else around, and Slickhorn Canyon's grottos and pools, when iced over, are one of the coolest things I've ever seen.
Last Christmas, we did row out in slush (more like shoveling snow than rowing) and agreed that one more night on the river would have seen ice dams.
We must've seen over 20 bald eagles and not another soul for 5 days.
The previous January, I did the upper section of the San Juan and it is also beautiful and has Bighorns. I prefer the lower section, but the upper section can be done in a weekend.
The ranger will know if the river is free of ice.
R/H is also cool in the winter, but not as cool, and takes almost the same amount of time.
There's always the Salt in February, but it's not a beginner run.
Have fun and get out there- I think too many boaters miss a whole new boating season when it snows!
"There is NOTHING--absolute nothing--half so much worth doing as simply messing about in boats. Look here! If you've really nothing else on hand this morning, supposing we drop down the river together, and have a long day of it?" -Wind in the Willows