When the weather gets too cold and/or snowy for tree work I go work as a ski patroller at the biggest, badass mountain on the east coast. Whiteface Mountain in Willmington NY, near Lake Placid. I offer... any expert skiers/riders want some let me know, I will be stoked to guide to the goods! Check out the slides on youtube. Anyways last year I worked in -26F first chair to summit. Never got above -10F all day! I also have been Ice climbing and backcountry skiing for over 20years.
My tricks. Must be fed and hydrated to start. When its cold start off the bat with all your layers, start to sweat out the door and you know your core is ready.
Layers:
2 base layers:a light weight one next to skin the a mid weight, on top and bottom. By the best stuff the cheapest. Most alpine wear is tough enough for tree work. TJ max has the best deals in town for leftover seasons, around october. I find marmot, cloudveil, northface all the time wicked cheap. Otherwise go online to like sierra trading post type sites.
Final layers: Soft shell, down jacket, and storm shell (all 3) on top. On the bottom storm bibs. All ways on the out side high performance, wind proof, water proof and BREATHABLE!
So here is the deal. You have to work. I over heat my core so that I can take my hands out of my gloves all the time when need be, I only wear kinkos with open gantlets! They are the best glove for your money hands up or down! Most patrollers use them, $20 at local hardware stores. Make sure you sno seal them twice over heat the night before the first day of use. Make sure you put your name on them first time some one else uses, them watch them. If it is 15F or colder I might throw a set of heat pads in them on the back side of the hand, perfect spot. With regards to my head, I hate hats, that said I am in an insulated helmet skiing. I will employ a fleece neck/face warmer when cold. For tree work I find the thinnest balaclavas I can to fit under my helmet, yes ski goggles from time to time when doing tree work in windy cold.
The secret is to feed and hydrate, over dress, regulate the core by removing layers as you get warm, re layer before you get cold when you slow down or stop for a while. There are also little tricks to get heat back into your hands and feet. I was a ski racer in high school, had to stand top of course in line wearing not much. Swing the arms and legs (not all at the same time)free from obstructions use momentum with the weight of your appendages not your muscles. You want the muscles relaxed at bottom of swing, you will feel warm blood being pumped into your hand when done right. The worst thing I see people do is hunch up their shoulders and blow into their hands, gonna lose that fight. I love the cold better then the heat any day...cause you can not escape the heat. You can work your body harder in the cold and barely sweat if you dress properly and regulate.