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I've not worked in those kinds of conditions. But when I've done manual, dirty work, I've used plenty of hand protection/barrier cream. Do they provide that at your work? Also, do they provide showers? I'd say to jump straight in after a shift so that your skin is clean for as long as possible each day. If you wait till you get home, it's an extra however long the commute is before your skin can breathe and recover.

A general moisturiser that I quite like is Aveeno 'body lotion'. It used to be called hand cream but they must've realised people will buy more if they use it all over. It stays on well. I've used it while decorating and doing 'ordinary' construction work. Paint and oil/grease wash off a lot easier at the end of the day because the muck doesn't stick to your skin so much as the layer of moisturiser. It worked on my face while painting ceilings, too. During ordinary hand washing, it's a small challenge to get it off, actually. If you're not trying to take it off, it'll stay on for a few washes. As Aveeno can be used all over and doesn't feel greasy (it will if you use too much), you can put it all over, where you might not want to use something 'stronger', like Vaseline.

Maybe Aveeno wouldn't be quite as good as Vaseline, as queermunist suggests. I prefer something like Epaderm to Vaseline but I'm unsure on the technical differences. It's inflammable, though, so don't use it if you smoke as you will go up in flames! Creams like Epaderm also get soaked into your clothes and will never properly wash out so they will always be easier to ignite, which may be a problem if you use any flames or any equipment that might spark (I'd assume that coal mining equipment, of all equipment, would be tested never to spark, but I can't be sure). For this reason a work-site barrier cream might be better, but I don't have any recommendations.

What safety gear do you have to wear? It's always worth wearing long sleeves/overalls/gloves if there's a risk to damaging your arms, etc, plus goggles and a mask to protect your face (I imagine this is all complusory in a coal mine but I thought I'd mention it just in case). The more you can cover up the better. Use a cream/Vaseline for what you can't cover up.