Might I first congratulate you with your procrastination skills. You are an expert, my dear fellow.
Considering the snow, I'd say you need snow boots. And isolating clothes, with loose clothing under it. And really important is a balaclava. and suitable climbing gear.
face it. YOU ARE LATE.
but:
in remote mountain hiking it's a good idea to wear heavier supportive boots to protect your ankles and feet. Walking with a sprained ankle on a day hike is inconvenient compared to trying to limp out of the back-country mountains with the same problem and a heavy pack. Thinking ahead and being prepared with the right mountain gear, guides, and information can literally mean the difference between a minor mishap and at times death. Take your safety seriously.
Depending on how cold the temperatures you might encounter are you'll probably want some good insulated hiking boots (depending on the altitude and temperature you may need mountaineering boots), hiking clothes, sleeping bags, camping tents, and other equipment used for hiking rated for lower temperature than what you think you'll actually experience. This will give you an extra margin of safety as will a hiking checklist. You might want to have a quick look at these hiking accessory ideas too.
Also keep in mind that mildly uncomfortable mountain hiking gear will become a bigger problem on long trips.
Is there possible snow or a glacier you'll be hiking over? Will you need crampons for extra traction? Are you mountain hiking below a possible avalanche area? Are you mountain hiking on or off trail?
Do you need a satellite phone or emergency beacon? How much experience does your guide have? These are just a few of the questions to ask yourself before you leave.
Difficulty: Research your mountain hike first and know the level of difficulty before you begin. Plan for and add time for distance, altitude, weight, and having to navigate if there's no trail. These will all effect your duration of time spent on your trip.
Duration: Always tell someone your itinerary, so they know where to search for you if you don't return on time. Due to harsh conditions, make sure to give yourself more time to cover the same distance.
Food/water: Consider how much food you'll need and then pack some more for an emergency. This doesn't have to weigh you down alot, even a few energy bars are better than nothing. Also make sure you have a way of getting drinkable water, whether that's carrying it in or using a filter or a purifier.
Maps: Maps are an important part of any mountain hiking trip. Even if you've traveled your route ten times in your sleep, a map gives you a good prospective if you have to take an alternate trail due to mother nature or if you happen to get off the main trail etc. They're light and don't take up much room. I recommend sealing them in plastic or other waterproofing to protect them.
Weather: This will vary from location to location, know your area and what to expect for that time of year and what possible surprises you might run into. Consider mountain hiking conditions and remember weather can change quickly. Make sure you have the appropriate hiking gear and equipment used for camping to keep you safe, dry, and warm.
While this is more mountaineering than mountain hiking you might appreciate this book by one of the greats. He gives a different perspective than the one the portrayed by "Into Thin Air."
Above the Clouds: The Diaries of a High-Altitude Mountaineer, 5/5 rating, by Anatoli Boukreev, Natalia Lagovskaya: Written by a Russian mountaineer who ascended 11 of the world's highest mountains. Includes pictures from the top of some of the peaks he climbed.
Good luck. You might just need it. or not.