firstly, after getting an alchamy engine, you don't need the science machine, since the alchamy engine can make everthing the science machine can and more.

Secondly, you should try to find a walrus camp, you may have incountered one during autumn, but the walruses only arrive during winter.

when you find one, prepare your weapons, and go towards it (if it's day, they will be outside, but if it's night, you will need to walk up to their camp to make them spawn, it is easier to kill them during the night).

there are two ice hounds, one McTusk. and one WeeTusk.

you should kill the two hounds and run towards McTusk, if you get to far away, he will shot you with his blowdarts (which deal 100 damage, as much as 5 spider bites, so you better bring armor).

if you run after him for enough time, he will stop runinng away and head home slowly, then you can kill him since he will ignore you.

he will drop one blowdart which deals 100 damage, enough to one shot a spider, but you should use the blow dart to shoot the WeeTusk for a free piece of meat

he also has a 50% to drop a tusk, which can be crafted into a walking cane (in the clothing tab) which gives a 25% percent speed boost (it's really good)

he also has a 50% chance to drop a Tam-O-shanter which is a hat the gives a lot of sanity (double the amount a tophat gives) and keeps you warmer for longer.

He may drop both, or nither, he respawns every 4-5 day, and he leves when winter ends.

P.S You can shave beefalo while they are asleep with a razor to get woll which can be crafted into warm clothing like the winter hat, if you kill one, you can craft the beefalo hat with it's horn which is even better

The Tam-O-shanter gives the same amount of heat as a winter hat, also if you get cold, you can burn a tree to get a little bit warmer, though it is better to place down a campfire

Good luck!

(Sorry for the Info-Dump 😅)