When I ventured out into the wilderness of Canada back in 2013, I would routinely go shooting in -20c to -35c air temperatures. I wore very low profile North Face Etip gloves. They are the type that have the foil on the index finger and thumb so you can use an iPhone, etc. They still allowed excellent use of the camera and my hands were reasonably okay in those when walking around. If the wind chill was particularly strong, then I would wear an outer mitten to keep my hands protected, or shove my hand into my pocket. You can purchase gloves that have an outer mitten section built in, that you can fold back out of the way, to allow your fingers to access the buttons. You can also get fingerless gloves with an outer mitt. You could wear those in combination with the North Face Etip type gloves which will give you the best of both worlds.
By far the biggest issue is the camera itself though. The cold from the magnesium alloy body of the D800 and my 300mm f/4 AF would radiate through the gloves, something fierce! I would highly recommend you purchase a Lens Coat and also a silicone skin for the body itself. This will provide an extra layer of insulation between the camera and your hand and certainly make things more bearable. -10c isn't as bad as it sounds and using either gloves and mitts or a combo glove should do the trick. You can of course use the little heat packs inside to add warmth.
I would also highly recommend a Peak Design Capture Pro, with the Pro Pad if you do not already own one. This allows you to mount the camera on your belt or bag strap, keeping it firmly in place. This lowers the chance of accidentally knocking the lens and also easy access to the camera. Nothing more annoying than wanting the camera in a hurry and you have to try and retrieve it from the backpack, then replace it when done to carry on moving. The Capture Pro takes all the weight off your neck and stops the camera swinging around. If you're walking through snow banks or climbing over small obstacles, it can be a godsend.
If you use a tripod, you can cover the tops of the legs in foam, if they don't have it already. Depending upon how thick the tripod is, you can use bicycle handlebar foam grips. Only two of mine were covered, so I did the third leg too, which detaches as a monopod. It can be a job to do it but, the best way is to use a small amount of dish soap to aid the insertion. If it's a tight fit against the leg, virtually all of this gets removed as you slide the foam over anyway but, makes a huge difference. The foam means you don't have to touch the cold metal legs.
If you wear glasses, I would also look at a Respro cycle mask. These are made from neoprene and do a good job of keeping your face warm. They also have a metal nose synch, which you can mould to your facial features. This prevents your glasses or goggles from misting up, as the air can only be exhaled from around the mouth area. That was one problem I had back in 2013. My balaclava was relatively cheap, leaving my mouth exposed. The moisture from my breath would rise as I exhaled, then condense on my eye lashes, freezing my eye lashes shut lol. I've also had success using a shemagh to make a headscarf/facemask. This kept my face warm, allowed me to breathe easily and my glasses never fogged once.