Can I clean enameled cast iron with steel wool?

it is perfectly safe to use stainless steel wool on a Vitreous enamel. I presume that the cast iron skillet has a Vitreous enamel finish.

The reason is simple: Vitreous enamel is essentially a type of ceramic and has a hardness of around 5-6 on the Mohs scale. Steel has around 4-5 on the same scale. This means that generally, you can not damage it with the steel wool. Also no not confuse the "grit" of the steel wool with its hardness :P

The only thing that will happen is that the enamel will get very small scratches and that things will stick a bit better in them. You can get rid of most of them with a good polishing compound if they disturb you to much.

Personally I would advise you "not to need" to clean it with steel wool in the first place, but is something burned up badly and you do not have heavy cleaning agents nearby steel wool is an acceptable solution.

If it is just for cleaning leftovers , usually soaking in soap water and a hard plastic brush does a very good job as well.

Remember that even thou Vitreous enamel is very hard and durable it may be damaged by overheating or crack if dropped.

I can't think of any use for steel wool in cleaning cookware other than getting rust off of cast iron. For just getting off stuck food, you'll be damaging any cookware you use it on. I use the same combo as Michael (non-abrasive scrubbing sponge, occasional Barkeeper's Friend) for most of my cleaning. Barkeeper's Friend particularly helps with burnt-on oil.

For cleaning enameled cast iron, all that is usually needed for stuck-on foods is to let it soak for a while in warm soapy water. I've seen recommendations for adding baking soda to the soaking water, but I've never needed to do it. If you've already managed to discolor or scratch your enamel, Le Creuset makes a polish/cleaner that is supposed to restore the appearance of the enamel. Again, I haven't yet needed to use anything like that to clean or maintain mine.

I'd recommend a regular scrubby sponge, and when it need a little deeper cleaning, Barkeeper's Friend cleanser.

Steel wool comes in different levels of abrasiveness but all are still quite abrasive. I'd avoid using them on enameled cast iron as it will likely damage the enamel. If you need to do it once in a blue moon, you'll probably be ok, but I'd try very hard to keep those instances as few as possible.

For non-enamel cast iron, other stuff will work just as well without pricking your fingers to death but the pan will be fine. I personally never use it because I don't wear gloves to wash dishes and steel wool hurts like mad when it jabs you.