I've got a zippo one, but I don't really use it much to be honest. It last more or less all day if you fill it up, even longer if you keep it insulated. But I don't find it that useful. It you keep it somewhere with easy access for your hands like an outside pocket, it barely even warms up. You have to keep it really insulated to get any heat out of it, which renders it pointless. Not to mention the weight of it. I think I'm going to sell it and just use the disposable ones instead.
I have to wear contact lenses as I have an eye condition that glasses are unable to correct. They're also the hard plastic type that aren't disposable, so I have to be fairly ingenious to clean them and put them in whilst trying to keep weight down on a camping/hiking trip.
What I do is carry solution in a very small eye drop bottle for an overnighter, or a slightly larger bottle for a few days. Anything over that, I'll probably just take a few bottles. You'll find that most contact lense/eye drop bottles have a removable top that allows you to wash out and refill them. I didn't realise this until I looked closely at them.
I also carry a light case, a very small plastic mirror, 1 non-alcohol cleaning wipe for my hands for every day that I'll be out + a couple of spares (lighter than carrying a bottle of that hand sanitizer stuff), and a scrap of microfibre cloth to dry my hands after cleaning the lenses.
If you are going to take dailys (which I would definitely do if I could), it's easy. Soft lenses are so easy to put in you don't need a mirror, and you can just take a few spares instead of a bottle of solution because they are disposable!
I've never had a problem in below zero temperatures, but I've never really done much in extreme temperatures. It might be worth storing everything in a small insulating bag?