I have never done the Lodore trip in Winter, but I know people who have. The water level is what it is, so it is not a super exiting trip. You can count on it being cold so plan for that. I would not want to do it summer or winter without raft support.
I have done Split Mountain in March and you still need a permit to do it. There is obviously noboby else applying, so it is no problem to get one. I am sure the same is true for Lodore.
I have also done Westwater in February. It was not bad except the paddle out got fairly miserable. Of coarse that's not really much different from summer.
I'm not sure how to know if they are free of ice. When I went down Westwater I went with some peole from Grand Junction. For Split Mountain I knew people in Vernal, Ut who told me the ice came off the river below the canyon.