We did Ladore in September and given the geography I would guess it about has to ice over. There are numerous canyons with steep walls and slow water (Can't imagine it gets much sun), not to mention the big bend area that could dam or freeze. Best guess is it maybe a torture. There is no easy way out once your in, and lines are already tight in the first days rapids without snow or ice.
Maybe check the park service site to see if they have any canyon temperature data or call a ranger, but my guess is it would take some serious luck before April to get sustained temps above freezing in the canyons. If you try it I would go at the last possible moment before permit season. Even low flows on Lodore would be worth it though! FYI, some of the areas may be calving range, so several camps could be off limits.
The up side of dam release is that it will be relatively warmer water, so as long as there isn't snow on the ground you'll probably be okay. I've done a Yampa the last week of March and it was great for all but the last day when it snowed.
The ice dams the get people stuck in Deso are when the White & the Duchesne send down floes that get hung up on the sand bars. While that might happen with the Yampa & Echo/Island Parks, I haven't heard of it being as big a problem.
I have done Ladore several times around Halloween. It gets pretty cold and dark already that time of year. I suppose the End of March is about as far from the Solstice so it might be comprable, but I would expect it would be colder still.
Dry Suits, Tight Spraydecks, Sleeping pads under your legs in your boat and you should be ok.. If not, paddle harder. You can do it in two days if you want to. Fun trip. Too bad it is so difficult to get a permit down there during normal times of year.
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