The reason they recommend wool is that it's lightweight yet very warm, can absorb and later release moisture, resists odors, tends to be very good at temperature regulation, and still provides warmth even when wet.
As far as I know, you won't find a synthetic that replicates all of wool's properties. The only thing you can do is pick what limitations you want.
Here's my guide:
- Underwear: You can try some windproof underwear (tell me if it works) or some synthetic underwear. Synthetic underwear tends to like to collect bacteria, so I hope you aren't prone to any crotch-area related infections. Cotton, if it stays dry, works, but once it's wet, you're in trouble. If you're male, think about putting a sock on it in cold weather.
- Base layer: Polypro does pretty well. It wicks moisture and dries quickly. Polypro long-sleeved undershirt and leggings works wonders. I've doubled up with polypro tights for colder weather. This is one of the few areas where the synthetic does work amazingly well. It's even what the US Army uses to prevent its grunts from freezing to death.
- Insulating layer - upper: If you're avoiding wool, I'd recommend one of the wind-stopping polar fleeces.
- Insulating layer - lower: You can try cross country skiing tights. They are synthetic, and don't totally suck. There's also thinsulate-lined jeans that are otherwise regular cotton jeans that are pretty warm. I'd be very hesitant to use them anywhere that I couldn't find shelter in a reasonable amount of time because once they are wet, the cotton will ensure they stay wet.
- Shell: The other place where being vegan isn't a disadvantage - synthetic windblocking, water-resistant shells are mature technology. Try to get one with vents if you can. Wind-blocking pants are great, and really increase the warmth. If it gets really cold, try actually throwing on a wind-proof jacket.
- Head: Synthetic balaclava, acrylic hat. One of these days I'm going to try a wind-blocking solution as well, but I haven't yet. Goggles are amazingly effective at preventing ice buildup on your eyes or eyelashes - if you're skiing or biking, this isn't a common problem. A decent pair should be resistant to fogging, and there's a substance called "cat crap" in the US which works well for resisting fog even further.
- Hands: Synthetic polypro liners, synthetic mittens, ideally wind-blocking. Have fun, like everything else, they aren't cheap.
- Boots: Not entirely bad. There are breathable synthetics that are moisture-resistant. I've yet to find a flexable sole similar to a mukluk in a fully synthetic boot (camuks have a rubberized moosehide sole, damnit). But the modern stiff-sole full synthetic boots aren't too bad. Get them on the loose side so you can wear two layers of socks.
- Misc #1: I find suspenders warmer than a belt. On the other hand, the metal clasps are nasty if they ever come in contact with bare skin. YMMV. Leg gaiters are great for trudging through snow, nordic skiing, and snowshoeing, and can easily be found in vegan versions.
- Misc #2: Hand/feet warmers: I've carried a few before just for emergencies. The non-reusable ones can be "shut off" by throwing them in a ziplock bag and forcing all the air out of the bag - they run on oxygen, and will stop "burning" when deprived of it. The reusable ones can be boiled to reset them. I'd suggest picking up a cheap pair of them just in case.
- Misc #3: A camelback, under a few layers, stays unfrozen. The hose tends to freeze up though, in a remarkably short period of time, unless you drop it under a few layers. Else you can try a vacuum thermos of hot water. Remember, water expands when it freezes, which destroys containers.
I left out socks and boot liners on this list because they deserve a separate rant of their own. In my personal experience, wool is king - it'll keep you warm, even when wet. So far I have a pair of suspiciously cheap Walmart boots that are full synthetics with an integrated liner, and have kept me warm when I'm active. I don't know if I'd trust them to keep my protected if I'm inactive. If you don't find integrated liners, bear in mind that the separate liners are almost always wool.
For socks, so far the best synthetics I've found are made from a fabric called "drystat", and run about $25/pair for heavyweight, knee-high socks. There may be cheaper synthetics that work just as well, but this is the one my cold-weather go-to store stocks, so it's the one I bought. I combine that a sock liner and a thick outer acrylic sock and it's worked so far. I'm not sure if it would protect me if my foot became wet. So be careful. Wool is king here, and I've yet to find an alternative I'd trust both dry and wet.
If your ethics allow, there's some used wool out there - wool sweaters aren't too hard to find at thrift stores in my area, for example. I know this isn't for everyone, but I'm throwing it out there are a suggestion. You may have to make a personal decision on some other stuff as well - some brands of winter clothing like to throw on an entirely unnecessary leather tag to display the brand - if you're a strict vegan, I could see this being something to avoid.
In short, being vegan and trying to find winter clothes for cold climates can be a challenge.
ETA: If you want to know my background, current temperature outside is a balmy 19F/-7C.
