I’m in Ohio.
I jog two to three days a week during lunchtime here at work. Each winter I wear the same thing: cotton sweatpants, T-shirt, and cotton sweatshirt. This attire doesn’t work very well; I am still cold, and the clothing tends to absorb moisture.
I am looking for recommendations on what to wear.
Cotton is bad because it retains sweat. You want more technical fabrics. I usually use a spandex base layer, and add some extra insulation and windbreak layers on top of that. The objective is to wick the sweat away from your skin so it does its job and gets out of there instead of sticking around and making you colder.
I run in tights (or thermal tights if it’s really cold), long sleeve polypro shirt, and windproof running jacket. I’ll wear a thin hat and gloves most times as well, but the gloves rarely stay on for the whole run.
Are you still cold after you get going, say 15 minutes into your run? I go for long walks in just about any temperature, and I’m never cold after my heart rate goes up. I wear long johns, a pair of pants, an undershirt/t-shirt, a sweater with a collar, and a wind-breaker jacket or a parka (depending on how cold it is), along with a pair of regular socks, a pair of Sorel winter boots, a pair of gloves, a good scarf, and a knitted headband. The gloves usually come off and the jacket gets opened before I’m finished walking because I’m giving off so much heat.
Maybe you’re just not wearing enough layers.
Another thing about exercising outside in winter is that once I come in from the cold, I have to change the underlayers before I go out again, or I will not be able to warm my feet up again. Moisture is the enemy of staying warm in winter.
When it’s below even 55, I add a light windbreaker. I have heavier jackets for colder weather. I add more layers of shirts as the temp goes down. I’ve been running in the Midwest for 47 years and the same program works every year, but I want to be warmer now. I don’t care how hot it gets or how much I sweat. You need a very good weather-cast or a selection of equipment at work. For a lunch hour run, I could run in anything that was not indecent.
I do my winter kayaking in synthetic long johns with a t-shirt and shorts. I add a hoodie if it’s really cold.
I’ve never had luck with a windbreaker or softshell - the wind seems to go right through them.
They say you should dress for 20 degrees colder than it is, so that you feel cold starting out and won’t overheat when you warm up.
Cotton is a definite no-no. No cotton. Get some good technical clothes and you’ll be much happier.
Goretex onesie - I have one from LL Bean, it’s amazing. Forget cotton - insulated wool or high-0tech fabric.
Layers definitely. Also head/ear protection, it can get cold here in Michigan (ha!) and most uncomfortable is having a freezing face and numb ears.
Here’s a helpful guide. You’ll need to determine if you run “hot” or “cold”
** A subscription pop-up comes up first, just close that
Do you mean 20 degrees warmer than it is? Cause that makes sense, and it’s basically what I do. 
Sorry, you should dress as if it was 20 degrees colder is what I meant.
Choose your attire carefully.
Many years ago, the NEJM was required reading at work. A short 1977 communication, “Penile Frostbite, an Unforeseen Hazard of Jogging” pointed out the dangers of cold weather jogging - to the great amusement of many in our lab. The article is available online if you subscribe, if not here is an article about the article.
I don’t mind sweatshirt + sweatpants in cold weather. After the first mile it’s pretty good, and I have run at 25-30F in the same attire you wear.
My biggest problem is my hands getting cold, so if I ever do this again I will get a pair of light gloves to wear. Some kind of head covering might not be bad either.
You probably shouldn’t jog in the snow. I did it once, and I enjoyed the crunch crunch crunch rhythm, but even the thinnest layer of snow hides all of the ankle-twisting tree roots and holes.
I heard “dress for the second mile” i.e., you will be cold at first. No cotton. I’ve got some synthetic leggings that are great but whatever they are, the lettering on the tag has worn out. UnderArmour? And fleece.
I should add, I don’t do the dress-for-second-mile bit. I dress as warmly as possible without being too weighed down, because I’m a cold-natured person.
I posted the link above but in the winter we get here (I’ve gone out as cold as -50 with the windchill) I generally wear thermal running tights, windpants, a thermal layer, running shirt and windbreaker. I wear a toque and a face cover (usually a balaclava or buff) and either dollar store gloves or running mitts, if it’s a long run.
Running shoes and tech socks (long ones, not the ankle style I wear in summer) and I am good to go. This way, I can unzipped the jacket if I need to. If it’s not windy, I can ditch the windpants.