Well, that what you describe is completely normal. You're probably wearing a cotton t-shirt while doing that. Even if you're not drenched in sweat, you are still heating up and perspiring when you're shoveling snow.
The problem with cotton, is that it loses about 80% more heat when it gets damp, whereas wool or symthetic will only lose about 20% or less. Towards the end of your shoveling, your body can no longer maintain the optimal core temps, since you're likely losing more and more heat due to fabric getting damp/wet.
Cotton is a terrible fabric for any amount of physical activity in the cold. Wool or synthetic is where it's at. Unlike cotton, synth fabrics and wool don't soak up nearly as much moisture. The moisture is wicked away from the skin and spread out over a larger area, which help the fabric dry much quicker while keeping the cold water away from your skin as much as possible.
My personal choices when I'm out for an extended time in colder weather are:
- upper body. Polyester compression thermal base layers, synthetic (like fleece) mid layers. Heavy outers if necessary.
- lower body. Either polyester or polypropilene base layer, synthetic outer
- feet. merino wool socks. light weight for summer hikes, mid/heavy for winter
- head. merino wool hat, if needed when cold.
Once I discovered that not all clothing materials are made equal, and there's a very definite right/wrong choice when it comes to which material to wear based on your given conditions, the cold weather outdoor experience was completely elevated for me.
You simply can't beat being able to have an intense hike in cold weather without being too hot or too cold, and then drying out fast when the activity stops.
Lastly, your scenario is actually deadly, had you not been at home. Wrong clothing will leave you cold after exercise, and if you happen to be backpacking and camping in the woods overnight, hypothermia is a very real possibility.