My short answer is probably not.
Long answer: In addition to keeping a horse warm, a blanket will also hinder winter coat growth. Most horses who have blankets during the winter are either rodeo horses or very old. Rodeo horses get blankets to keep the winter coat to a minimum so that they are easier to brush and saddle and so that they cool down better after a run. Horses are naturally equipped to handle the cold weather. Non-rodeo young horses who are blanketed are often owned by people who don’t understand these things or do so for looks. (Let’s face it, they are prettier when they aren’t so hairy.)
I’m in NE Oklahoma. A few years ago we had some seriously low temperatures (it barely got over 0 during the day) and I blanketed then, in addition to bringing my horses in. Otherwise, they can handle the weather. I also ride all year and try to keep up training, but I don’t rodeo consistently, so I want a good winter coat on my horses.
If this horse is elderly and is outside shivering, then he’s either too old to handle the weather or has been blanketed a lot in the past and has stopped growing a good winter coat. If he doesn’t have a good coat, he may also just need wormed, or he may be needing something in his diet. Either way, then if blanket, also.