For the OP - in your case and in TN, I would recommend that you put a rain sheet (rain turnout sheet) on your horses (instead of a turnout blanket) when it's cold and wet (rain or snow or fog). When it's just cold (cold and dry), they likely need nothing at all (because you reported that they have nice winter coats). I would think that for you in TN, a rain sheet would be enough even in winter. And you'd only need to use it for cold + wet. (I also will use my rain sheet when it's cold + super windy (gale force winds) I use it as a wind breaker). But if it's cold and dry, he just uses his fur and gets extra hay to eat.
For the second poster (and anyone else...) - be careful covering your horse when damp. The main issue in our area (MD, USA) is rain rot. Rain rot typically is something that folks in balmy climates have to deal with (tropical FL USA, for instance). However, we also have to deal with it here. Some horses are prone to it, others are not. Rain rot comes from a bacteria that lives in the soil. Horses who are susceptible to it develop these sores on their skin. (It looks like a fungus eating away at your horses fur). It's not life threatening. It's just a pain in the neck and can be very painful for the horse. Rain rot tends to flare up (for susceptible horses) when they are both damp and hot. So even during cold times (winter), if you put a rain sheet or a blanket on a damp horse, you can end up with rain rot (sheet/blanket makes the the damp horse warm. Rain rot ensues!)
So when your horse is damp and it needs to be covered (various reasons for this), I concur with the need to use a Cooler. I also wholeheartedly agree with the comment above about not using a cooler made from a synthetic material for this purposes. (The synthetic fibers trap the moisture and create the dreaded damp + hot scenario that leads us right back to rain rot). I'd love a wool Cooler! (I didn't even know that that is an option. Awesome.). They used to make this awesome "Irish weave" cooler. (They likely still make it, but it's not "in fashion" right now. Therefore, I've been finding it hard to find these last 2 years). It's a cotton weave -- it has little holes in it (sort of like mesh looking). If you run across one of those, grab it!
(I once found one at a Horse Symposium and thought I had won the lottery. However, it turned out to have been manufactured in China and so the size was not at all the normal size. It also did not appear to be cotton...).
As for brands -- I'm also a Weatherbeeta fan. That said, I also had never heard of Schneider's until a post here on Horse Forum. They look like they have fabulous stuff. Therefore, if others are recommending them, I'd give that a try too. I also agree that Tough1 does not hold up. However, they are a good price point. Therefore, if you're not sure what your need, it's not bad to spend a smaller amount of money on a Tough1 that you might use only for one season while you then figure out what might be better or more useful to your needs. (As opposed to laying our serious money for a Weatherbeeta and then discovering that the item is not what you really need...) I'm going 3 seasons strong on both a Weatherbeeta rain sheet and a Weatherbeeta medium weight blanket. I expect them to last several more seasons. I use the rain sheet a lot, because my guy gets the rain rot. Sigh.
Hope this helps.