Nothing warms like wool, and it does pull moisture from the coat. But wool coolers tend to hold moisture in the fibers, so they don’t themselves dry very quickly (and can also get heavy with moisture). If you use one on a wet or sweaty horse when it is really cold, you may need to change it out in 30 minutes to an hour so the horse doesn’t get chilled from the retained moisture in the wool fibers.
Fleece coolers warm, and wick, and dry pretty quickly, so there is far less chance of the horse getting chilled.
I have an Irish knit cooler that I use on moderately cool days if the horse is a bit sweaty from work. It isn’t quite as warm as a fleece cooler, but it wicks pretty well, so my horse stays cozy while he dries.