So you want to start training outside in the winter. I have some suggestions that should make it more comfortable. As a general rule, wear multiple lightweight layers you can remove and replace to reduce how much you sweat. Wet = Cold
Hat - Any hat will do. I do not recommend headbands because of how cool the top of your head can get. No one is going to judge your winter hair.
Neck/Face - Depending on how windy it’s going to be, having a tight scarf (neck gaiter/face shield) works great. You can keep your throat warm and move it up to your nose and mouth if you need it.
Shirts - In order from inner to outer. (1) Skin tight breathable layer that won’t absorb sweat. (2) Tight thin fleece. (3) Thick fuzzy fleece/sweatshirt to trap heat. Zippers are always better so you can easily remove or vent if you get too hot.
Jacket - A thin water/wind resistant zip up with a hood works great instead of a thick puffy coat. The first layers tight to your body should keep you warm, not the jacket, which enables you to open and remove the jacket without drastically changing your temperature.
Gloves - Cheap thin knit finger gloves that you can buy 2/$1. They block the wind and still allow you to feel the objects you’re gripping. As a bonus, when you scrape holes in them you simply swap hands and get more use out of them without destroying nice gloves or breaking the bank.
Pants - In order from inner to outer. (1) Skin tight fuzzy pants. Women's (yes guys, ladies pants) tight pant/sleepwear are very inexpensive and warm, and best of all the crotch isn't so low that it restricts your legs and it's tight enough to stay up. (2) Comfortable sweatpants. (3) Optional wind/water resistant thin shell. In my experience, rarely do my legs get cold, but you can mirror the same layers as noted above for shirts as you do with pants to stay warmer. I like to be more comfortable running and jumping as multiple pant layers can be very restrictive.
Socks - If there’s a chance your feet will get wet (lots of snow) then 2 pairs of socks with the outer pair being wool works well. I usually wear one pair of standard cotton socks.
Shoes - Non-mesh upper so water can’t easily get in and aggressive traction to provide resistance from puddles and snow. Trail running shoes work great but whatever you are comfortable and warm in works best. If you can jog and jump properly in your normal winter boots then use those!
Winter Training Tips
Your body does a great job at regulating its own temperature, so let it! If you’re going into a situation that you know will be cold, telling yourself repeatedly, “it’s so cold, I’m so cold, it’s so cold...” will not help. Instead, relax into the cold and allow your body to warm itself. We can trick our body to generate more heat than it needs by exposing it to colder temperatures than the immediate environment. More about this method is discussed during outdoor winter classes.
Bring a backpack. Outdoor winter classes cover a lot of ground and use different locations, so have a backpack to hold extra items and pieces of clothing. Chapstick and water should always be packed. If you have one of those nifty insulated water bottles, it’s nice to fill it with warm water. Packing an extra pair of thin knit gloves is handy in case yours get wet.