In looking at Google, it looks like rusting is quite common.

In another vein it was mentioned to put potpourri or something similar for smell purposes.

I have one, but I set it on an iron trivet. It will boil off very quickly if you set directly on stove. I do fill mine every night.
And yes I get rust inside. Occasionally I take a steel scrubby and clean it out good... maybe once or twice a year. The rust really doesn't bother me.
I also put scented oil in mine. Sometimes I make a cheese cloth bag of cinnamon sticks, cloves and dried orange peel. That last several days.

Water will cause rust on any kind of uncoated cast iron.

We had one shaped like a dragon and used it flat on the stove. He was cute with steam coming out his nostrils but I don't think he added a lot of moisture to the house. Eventually, he rusted through and started leaking. Now I just use a 2.5 quart pot, Farberware, on a trivet, no cover. We fill it whenever it needs water, usually twice a day.

The one we had was enameled cast iron - that solved the rust problem but we did still had to fill it frequently.

You'd be best to invest in a trivet to go under your pot/kettle. Our woodstove has a rust spot from where our kettle has boiled over/out the spout. The water will still boil, and sometimes spit/boil over, but your humidifier won't be sitting in direct contact with the water. Our woodstove has a glass front door, which had spitting water pour over, but luckily the glass held up to the thermal shock. I am very careful now to not over fill the kettle. When funds allow, I will be investing in an enameled one, as we love the extra humidity in here as we heat with wood. Any of the cast iron ones friends have are all the same eventually..rusty red and rather grotty looking if upkeep lapses.

Cinnamon sticks or even vanilla are randomly added to mine. Love it, but hate the burnt smell if the water boils dry and the cinnamon sticks (which as pointed out on a different thread, probably aren't real cinnamon) burn. I fill our 2 litre kettle 4-5 per day as needed. Enjoy!

Thank you for all the comments. I do have cast-iron trivet I can use. That wouldn't have occurred to me. Nor did I think about adding natural scents. Great idea!

My favorite stove top blend consists of orange peel, whole cloves, and a cinnamon stick.

In areas where it gets cold, all heating systems result in the heated air being dryer, and where it's really cold the relative humidity can get as low as on the desert ... which causes trouble with furniture getting wiggly or unglued.

In cold weather areas most of us need supplemental humidification.

I put empty food cans with water in them beside the floor registers where heated forced air from the furnace comes out. I could put them on the register, but that would impede the air flow, resulting in reduced heating efficiency, I think.

ole joyfuelled ... but joy only offers marginal help, if any, with wintry warming

OJ, I'm guessing you don't have cats or dogs. In my house, they would a) drink out of the cans, and/or b) knock them over. :-)

Interesting solution, though.

Now that I'm enthusiastically using the humidifier on my woodstove, I remembered that I don't want the air to get too humid, especially near my piano. The piano does better if the air is a bit dry. I'll have to pay attention to the higher keys, which usually indicate if there's a problem.