If your horse is shivering, then they are cold and something needs to be done. If your stalls are open and can't block the wind, then putting a wet horse in is only going to marginally help. They are still going to get chilled. Your really need to cut the wind and blankets are great for that if you can't otherwise.
As much as us northerners like to on-up on how cold it gets, a brisk -40 is very different than a raining and windy 0/32. Cold but dry, still air is way more tolerable than wet and windy. The only times I've ever seen my horse actually shiver has been when it's been cold and wet. I've had him in his medium weight blanket (the one he usually wears when it' ~ -20*c/-4*f) when it was +5*c and he was still shivering because it was 2-3 days of cold, wet, rain/snow and wind. He's even shivered in the summer during a cooler thunderstorm when I couldn't get out to put his sheet on. (Meanwhile, my QH was happy as a clam in both instances)
Yes, blankets will flatten their coats, but that's why blankets have fill. To replace the air gap that the coat would normally provide. If they are too cold with just a shell, then put a liner underneath or a turnout with fill on. I'm not a fan of using coolers underneath as coolers will usually stretch and pull if left on for a while. Some do have reinforced shoulders, though.
It's not all or nothing, you can blanket some days but not others. Contrary to what some people will have you think, blankets do not damage their ability to regulate their temperature, their ability to fluff their coat, or the growth of their coat. Once you pull the blanket off, they will fluff up as needed after (humans still get goosebumps despite us wearing clothes all the time). Some might be little sissys about it and realize that they like being warm,
Sometimes I think it would be easier to be in a climate that snows rather than just being warm enough to not snow and the horses get soaked if they are not covered in some way.
Honestly, it's really nice in that way. Once it gets below a certain temperature you can pretty much put any blanket on them and they will be fine. A too heavy blanket might make them a little warmer than ideal, but you won't sweat or overheat unless they get silly and start running.
I'm of the opinion that a blanket is better than stalling any day. I would opt to blanket a shivering horse rather than keep them in.
When the horses were still out on pasture, we got some cold, wet days. Some of the horses would get blankets, some wouldn't. It was pretty common to see the horses with blankets would be out grazing while the ones without blankets were standing in the shelter.