The average cooler is a thin these days, I wouldn’t expect it to add much – maybe 50-100g. The heftier Rambo wool coolers would likely add 150g-200g if paired with a windproof/weatherproof blanket.
I have totally done it in unusual circumstances, like Texarkana said – but even fleece coolers tend to stretch and pull back a bit over the shoulders and withers when worn for more than a day. They are just not made to be worn 24/7. It is not a permanent solution but it sure beats buying another blanket for those weirdly in-between fluke weather days, especially if you are a boarder limited to a certain number of blankets or limited space. When you have a whole herd to outfit, it doesn’t make much sense to buy a heavy weight (for example) for every single horse when you’re likely to only use it one or two days out of the year. I’m all about less is more - my horses have rain sheets, 100gs, and mediums - that’s it. The mediums stay on the shelf most of the year, and if I ever find I need a heavy, I either layer the 100gs with the mediums, or use a cooler.
I’ve done it when it unexpectedly snowed or rained and the blankets were in the wash, a blanket was soaked through, or, one year when it dipped below 0F with whipping winds in November! None of my herd really had much of a coat yet.