I have actual experience of this. A few years back I was given a couple of Suffolk ewes by a neighbour which hadn't been clipped for 3 years. I hand clip mine so I thought I'll just see what the score is and deal with it. As the wool was already risen it came off with no more trouble than a one year coat but because there were 3 coats all meshed together the weigh of the wool actually made them easier to clip as it was heavier..... the wool crop was no use of course.
Your main problem with several coats of wool is that they may get overheated in the summer or get stuck on their backs and not be able to regain their feet. At this time of year they have absolutely no chance of re-growing a decent coat for the winter so don't clip them. No overcoat you could buy or make will have the same insulation properties of their own fleece and as they have been used to being toasty warm under their double coats they may well get pneumonia and drop dead within a day or two if you clip them now.
Leave them until summer but get them clipped in late May/early June depending on the weather. They'll probably leap around like spring lambs once relieved of the extra weight, mine did

They had a hair-cut, foot trim, vaccination and wormer, then ran up the bank and leapt over the fence to get back in the field with the neighbours horses where they had been before
Just keep an eye on them to make sure they don't get stuck on their backs and they'll be fine for the winter.