Carbon fiber can take quite a hell of a beating, both in terms of environment (water, sand, snow) and temperature. I've heard a lot of people discussing or complaining about how carbon fiber is susceptible to extreme cold, however I think most of it is hearsay and speculation.

There are only a couple times when I've read something regarding carbon fiber being fragile at cold temperatures...but the use of the word "cold" was always lacking. You would need to spend a night out on the frozen ice pack of the most northern reaches of Alaska during the heart of winter (which is actually what all of the verifiable accounts of broken carbon fiber 'pod legs I've read described...usually in relation to photographing the auroras) to actually experience cold enough temperatures for it to actually pose a serious problem. Most carbon fiber tripods these days are multi-layered, weaved or braided, and resin-reinforced. In the average case for cold, you may crack a layer if you slammed a leg with enough force, but it would take a pretty extreme freeze, well, well below zero, to run the risk of actually cracking a leg all the way through or shattering one completely.

As for precautions, if you are using your tripod at -20 or below, you need to make sure you don't slam it or strike it with anything hard. Dropping your pack or bag on hard snow pack or ice with the pod strapped to the outside is a sure way to crack or shatter it at extreme temps. You can crack a leg by pulling it too hard when setting it up, so you need to be careful with that as well. Section releases can ice up, and wrenching them too hard at cold temperatures may cause cracking, so its best to ease into it. Better yet, extend one or two of the sections before you get out into the extreme cold, and only extend the last sections if you absolutely have to (most of the articles I've read on aurora photography seem to indicate that you'll probably be sitting in a chair anyway, so full extension is often not required in the first place.) Once set up, you'll want to make sure you don't slam any of the legs with anything hard...such as the camera, any other gear, a flashlight, etc.

If for whatever reason you DID shatter a leg, I don't know of any specific health hazards. I've always heard carbon fiber was a pretty stable, safe, environmentally friendly product, so I wouldn't worry about that. Its unlikely it would break cleanly, especially if you have a layered product like a tripod leg. Its likely to leave a rough edge, so I would be aware of that and make sure you don't scrape your stab yourself with any broken ends.