Yes a cool mister will help, though run at high speed it's going to make a mess.
I run water soluble cutting fluid very lean on the grinder. I'm using Trim Microsol 585XT at about 1%, though that's just what I happen to have around the shop. When used this lean it can go funky if it sits a long time. That's true for most things diluted outside of their normal range.
I wouldn't use simple green for this. That's a pretty strong degreaser, it will get aerosolized and I wouldn't want to breath the mist or get prolonged skin contact. I'd stick with fluids designed for long term operator exposure and things like Trim are pretty safe.
You can use just water, I frequently do, though you'll get flash rust on things like O1 and 10XX steels.
Many belts do not play nice with the wet. Be aware that if you're getting black junk building up on your platen it is also building up on your belt, and it contains abrasive grit. It can cause rapid erosion of the platen, typically in grooves that are hard to get rid of once they start forming.
Another thing to investigate would be a chilled platen. I can tell you that as soon as I get my new mill, I will probably be making one for myself.
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A platen chiller is helpful, but the main use for these is for platens that get really hot such as radius platens and when running with the top wheel removed for lengthwise grinding and grinding in production environments. I run a chiller with ice in the bucket to keep the platen cold and it does help, but it's not the same as running wet.
If you do make one, be aware the path needs to meander back and forth. If the water path is straight there isn't enough turbulence and cold water goes in and cold water goes back out without picking up much heat.