I think this article is pretty on point - Horse Blanketing Questions and Answers from EQUUS Magazine | EQUUS Magazine
I think your idea for a cooling sheet is a good one. I've never delved into that area of things myself, so I can't recommend one. I should probably get one "just in case" though so I'll be watching what others have to say!
As far as the rain sheet goes, I hesitate to agree with you. [does he have shelter in his turnout/pasture area?]
Yes, being wet and cold is a bad combo. Yes, if he were mine, I would want to provide protection too. Yes, a blanket is a good idea.
The thing that keeps a horse warm in cold temperatures is primarily the loft of their hair. Heat generated from digestion plays a role too, but hair loft is a biggie - it's why wet horses have a hard time staying warm, wet hair can't loft!
What happens when you put a blanket/covering on top of lofted hair? The hair is weighed down and potentially/probably loses a portion [if not all] of its lofting potential.
Therefore, because you are removing hair loft from your horse by putting a blanket on him, it's important to replace that missing loft with blanket fill. A rain sheet, without fill, won't replace hair loft. It will smoosh down the hair in various areas without replacing that heat loss.
In my opinion, you should choose a heavier weight waterproof blanket if your plan is to use it when temperatures are near freezing, or below. You need to choose a blanket with more fill to replace the hair loft he looses by having a blanket on. Basically you're taking his hair-abilities away, so you need to replace that hair somehow. More fill means more replaced hair.
A thicker blanket also has the side benefit of not getting soaking wet as fast - I have a selection of rain sheets and I have yet to meet one that is truly waterPROOF. They seem to tend towards being water resistant which is great...until it's 35*F and your horse has been standing out in the rain for 12 hours, his blanket is soaked through, he's totally wet, he's shivering, and you feel like a real jerk.
At least with a heavier blanket, you have an extra safeguard against the blanket getting soaked through [plus he'll be warmer and happier!].
You will get a lot of varying opinions about rainsheet or not. Some think a rainsheet is just fine no matter the temperature if your horse has a good winter coat. And that's just fine, to each his own.
I just know that in the wet state of Oregon, a rainsheet at near freezing temperatures does not ever cut it.
I have a variety of blankets for my gelding [mostly inherited from my last horse because, luckily, they wear the same size!
]. He rarely sees any of them, of course, because [unlike my last elderly horse] he spends most of his time being too fat and not caring about the weather.
However, when he does start caring about the weather, I have one of these and really like it a lot: Tough-1 600 Denier Turnout Blanket - Horse.com
I had always avoided Tough-1 in the past because I thought they were cheap junk, but I have been really impressed with the fit, details, and craftsmanship of this blanket. It's, for the most part, much better than the Weatherbeetas I used to only ever buy!
I also have a 400g Pessoa blanket [talk about fancyyyyy] for his heavyweight blanket and, despite being over 5 years old, that thing has zero signs of age. But it was well over $200 new [I got it during a clearance sale for 60% off!] so I'd hope it was built to last!
Good luck! Blanketing can be really tricky, but rewarding!