I assume they are recommending the no-bows for wear overnight. I’ve used them before my horse recovering for a torn RH extensor tendon. They didn’t seem to do any harm. Any thick-ish bandage is going to cause the horse’s body heat to get trapped. The Back on Track maybe a little more than regular standing wraps because of the material thickness and composition. Their premise is that they help by stimulating blood flow (which results in heat), which is generally good in healing soft tissue injuries in the extremities, because they are areas with much lower blood flow and therefore prone to heal slowly and poorly.
The ice and cold hosing are not related to the actual healing of the injury, but reducing swelling, so that there is no scarring, the blood can get to the area that’s damaged, and the tissue fibers will heal aligned parallel so they slide across one another, instead of crossing where they are weak and will likely re-tear.
It’s most common to use cold on soft tissue swelling, but plenty of vets will sweat out stubborn swelling in the legs as well (Fura-zone, DMSO/Dex, Surpass, etc.).
They may simply be suggesting the wrapping for mechanical reasons. When you have a suspensory strain or tear, it can do a lot for the horse, just to take some of the pressure off by giving them some support. Depending on exactly where the injury is, I’ll wrap mine clear down to the fetlock and snug the wrap under the ankle to help give them some extra support with the weight on that leg while it’s weakened. This is actually the same thing that the BOT exercise boots are designed to do, if you want to take a look at pics of those and mimic it. 
I love those boots (or several brands make a knock-off version without the fancy material) when you start rehabbing. Or use the same shaped wrapping technique with track bandages or the cotton-lined elastic Eskadron bandages. (Don’t get the rubber lined polo-ish bandages - they stick to themselves in the wash and then tear when you try to pull them apart).