We don't stop for winter! Here's kind of a disorganized brain dump:
For day hikes, there are only a few specific trails I'll do solo, because I know them very well and they're very heavily traveled. Otherwise, minimum of two people. For backpacks, minimum of two to four depending on where we're going. If Una_dogger and I are just going to plop a tent down in the Pemi, that's very different from 3 days in Baxter, for example.
Gear for a day hike? My gold standard is being able to survive the night if injured. Between the members of the group I try to have a stove and pot, extra food, a gore-tex bivy sack to keep dry a sleeping bag, a down jacket, hand and toe warmers, and a headlamp with extra batteries (carried in an inside pocket to keep them warm).
Besides that emergency gear, I tend to bring more fat-laden foods (which keep you warm), more layers (to change into dry ones from wet sweaty ones), and I like to carry a 12oz thermos of hot tomato soup.
Almost always in midwinter, snowshoes are required and are generally on my feet. I take crampons for any trip that will have some exposure, though if the entire journey is expected to be sheltered by trees or not have any steep icy portions, I can leave them behind, since MSR Denali Evo Ascents have a pretty aggressive tread as it is. If I might be crossing an open snowfield, or dealing with very steep conditions (backside of Cannon, or the Hancocks, come to mind), I'll take my ice axe, too.
I like plastic boots. They're tougher to hike in, but they are 100% waterproof, which is a big help when using snowshoes since snow likes to accumulate on the top of the boot and slowly sink in with leathers. Plus, if overnighting, put the liners in the sleeping bag with you to keep them warm while leaving the shells outside.
And to answer your specific questions on tools, bottles, packs:
Any pack will do, but I try to bring one that has the ability to hold either snowshoes or crampons on the outside, plus ice axe. It also has to have plenty of interior space for all the extra warm layers, and finally I make sure it has an accessible location on the outside to strap a water bottle cozy. I currently alternate, depending on conditions, between a Gregory Chaos and a Dana Designs Bomb Pack.
For tools, I guess you could include the stove as one. Crampons, snowshoes, ice axe, all depending on conditions as I said earlier. And by ice axe I really mean mountaineering axe, not an ice climbing tool. Oh, and trekking poles *with snow baskets* are very helpful in soft conditions. Always a headlamp, too, given the short days.
And finally for bottles, I simply use the same hard-shell 1L Nalgene bottles as I do in the summer, but I tuck them into cozies like
this. One (or two) gets boiling hot water in the morning and is stowed deep in the pack. The other gets warm water and gets hitched on the side of the pack. Don't forget that winter air is more dessicated and you'll need more water than the summer. I like to add a little bit of Emergen'C (or the Trader Joe's version of it), too.