Nope, not a good idea.
A blanket (no matter the weight) is going to flatten down the hair that a horse needs to raise to keep warm. Therefore, if you just stick a rain sheet on your horse you're going to be effectively incapacitating their natural ability to use their own body heat to warm themselves.
The reason blankets are different weights (different amounts of fill) is to replace the amount of heat that would have been collected by the hair, had it not been flattened by the blanket.
If you blanket appropriately for the temperature (aka blankets of the correct weight/fill level for the temperature) your horses will be warm and dry. If you just stick a rain sheet on, without a thought to the outside temperature, you'll be making your horses colder than they already were. Horse hair does a great job of keeping the hair layer closest to the horse dry, so even when the outside layer is soaking wet it's likely that your horse is actually feeling dry.
As long as they have plenty of hay and shelter to access if they need it, they'll be fine.
If you really want to blanket your horses, go buy some cheap blankets that are correct for the temperatures you're experiencing. If you take the time to look, it's not hard to find something for $50 or so (sometimes under if you look for "Tough-1"s).
Good luck! I completely understand about hating to see horses standing out in the rain. I have the same concern so I blanket my mare all winter. :)
Fabio - 13 year old Arabian/Lipizzan gelding
Hazel - 14 year old Angora goat
Atticus - 4 year old LaMancha/Alpine cross goat
Rest peacefully, Lacey.