The mid season of snow shoe hunting the temperature is going to 20s and below. Keeping warm during these hunts can be difficult because to get in the action you have to move long distance fast building sweat. Then you stand waiting for the dogs to circle it towards you really cooling you off.
The ride to get to good snowshoe hare country can be long you don't want to sweat on the way. Don't dress for the hunt until you get there. The best method is to dress in base layers with a long sleeve shirt and carhartt pants for the ride. Wear shoes or light boots on the way. Just to keep from sweating.
Once on location you want to have outer wear that is easy to get on so you can get hunting sooner. The less fussing at the truck the more hunting.
Boots and socks: Get socks that are as close to wool that you can. Wool will keep your feet warm even if you sweat a little. For boots you want a rubber boots to the knee that has flexibility not stiff like most of the hunting style rubber boots. The lacrosse burly insulated boots are a good choice. Lacrosse boots also go very good with a pair of snow shoes when the snow is soft.
Pants: lined carhartt pants are more breathable the wearing long johns and with a pare of mule bibs on over them you will be warm. Mule bibs will keep you warm and dry they are water resistant making so they also keep the wind out.
Body: No need for a long john shirt a short sleeve and long sleeve shirt will do. For a outer layer a sweat shirt and wool jacket work good tacking the jacket off or unzipping when your to warm. The bibs will cover most of your upper half keeping mostly worry free from water and wind.
Hat and gloves: A baseball cap is a good idea as most of the time that will be keeping your head warm as a beanie is to hot. Keep a beanie with you one that is on the thin side you don't want a really think one. Get a pair of thin gloves like kinco's that will keep you warm and able to shoot. Also sunglasses are very nice to keep with you because of the brightness of the sun off the snow.
Bag: L.L.Bean makes a nice game bag that makes layering and carrying stuff easy on the go. Just keep hat, gloves, jacket or anything you need to get to in the game bag until you need use of it. When you start filling the game bag the vest has lots of pockets to switch your extra items to.
Stay warm and hunt long.