Pun intended :P.

I hit day 22. Winter is starting, taking me totally by surprise.

I'm rushing out to get a huge reserve of wood when that redneck walrus, his son and two hunting hounds give chase, quite persistently.

I have a spear and a backpack... They hunt me across the map and finally surprise me and shot me dead while I'm desperately trying to cut some wood.

Guess I'll need a more potent weapon by day 22 on top of prepping for winter.

The difficulty of this game just cranked up significantly.

Unless you're very lucky, you'll be hard pressed to find a better weapon than the spear.
What you need is an armor! Even lowly grass suits (IIRC, 10 grass + 2 twigs) soak up 60% of all damage directed at you, but I'd advise going for the log suit (8 logs + 2 ropes) which takes 80% of all damage and lasts considerably longer. (If my character has 150 health and a log suit, I can normally take on a L3 spider den and survive.) Sure, it takes the body slot, but I just keep it in my inventory, switch the backpack for it when fight is imminent, then pick up the backpack again when it's all quiet.

Also, it's very rare that you meet those walruses - in my quite a few games, I've only seen them once (I've seen their camps more than that, though).

60% damage reduction for grass padding? Holy cow! I don't know what kind of grass they have in his world, but I want some! That explains a lot. Thanks.

Kind of suck that I met the Walrus almost as soon as I got off my base on the first winter day then.

I was desperate looking for bisons, but only found a mammoth so excrements came in very slow for that game and most of my time was spent securing food.

If I were you, I wouldn't set up camp near a walrus igloo (which is just a circle on the ground in summer), unless you're already prepared. They can get pretty nasty. I once had three of them on my tail at once, since there were three igloos on the map (and I didn't think they were that close to each other, but they still were annoying).

If you can find a swap early on, quickly run in there and grab lots of reeds. Then after you survive a hound attack or two and you get some hound teeth, the blowdart makes for a great weapon against the walrus - two hits from memory and he's gone! Other weapons aren't viable since he runs from melee weapons and then pegs you from range, although if you have an ice staff you can freeze him and then jab him once you've killed his pet hounds.

Camping near a walrus igloo makes it easy to harvest hound teeth. Still, I would advise not to camp too close, as especially the first winter can be challenging with the hunting party around.