There are many hostels, each of the cities you mention have a few and likely more than one open through December.
So select your hostel, based on what you find online, in a guide book or from people you know who have been there.
Next read reviews, there are at least three sites that list most hostels these days, each will have reviews and besides, enter the name and location of the hostel and add review.
If you are looking for details like lockers, it helps to search within the page on 'lockers' (contrl F will often work for that.)
Whether you can leave your things behind for the day depends as much on what you bring as on the locks of the lockers.
I used to leave a backpack with 2 weeks worth of clothing and almost nothing else, and if there was no safe place I just left it in the room. But my camera was with me all the time and I would not even leave it in the room to take a shower.
If you bring a laptop, smart phone, expensive camera, money or passport, make sure you have a very safe locker. But better have them with you at all times.
Whether you want to take a sleeping bag depends on how many blankets (or how warm a duvet) you use at home.
I use a winter amount of blankets even in summer but when using hostels in winter I just ask for an extra blanket and am alright.
But if you are not used to cold weather, make sure you wear enough clothing when outside.
If you are from a warm or even tropical climate, you have no idea how cold cold weather is and how draining of your energy.
December in these cities if often as cold as being in the fridge for hours on end, but it can also be as cold as being in a freezer for as long as you are outside.
Clothing bought in the tropics is never warm enough, expect to want to buy more when you are in Europe. Iceland/Reykjavík has very nice but also very expensive cold weather clothing.
If you find yourself in need of warm clothing but only for a short time, talk with the people of the hostel, you can often buy second hand or even use 'left behind' stock.