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.
"I plan to leisurely advance through my existence" - Terry Fuhrman 1991