I use Armillatox Moss & Outdoor Cleaner. I find it works well on my lawns, patios, sleepers and tarmac, it is soap based so is not harmful. The first year I used it spring and autumn, since I have used it once a year in the spring. Apply when weather is dry, in the evening when no one will walk on it till the morning and after a few days I find the moss is dead and the slippery area is safe again.

Household soda crystals will work too, and much more cheaply - you sprinkle them on the area, leave for 48 hours, then brush over and rinse off.

Wow! Do you crush them first?

Moss always returns! I use Algon which is an organic based cleaner that you dilute and either put on with a watering can or sprayer - the sprayer being more economical. It is safe to use near plants and animals -though can scorch the grass a little if you spill a lot on your lawn.
It can be bought from most garden centres. Because I needed a lot at one time I googled the manufacturer and had it delivered to my home. Each 2.5 litre can costs around £6/7 depending on supplier and once diluted will cover 60 sq mtrs.
I do my patio area and my tarmac tennis court most years, it takes away the algae and grime but takes a few weeks to show a clean effect though the slippyness is removed within a week and the moss dies very quickly. I have tried Amillatox, I find it very smelly and not as efficient as Algon.
Try it, it is brilliant and needs no scrubbing. Ask at your local garden centre as they have this same substance often under a different name and a little more expensive.

Steragram: No, you don't need to crush them, you obviously haven't bought any recently - about 5 years ago, they changed - although still sold as 'crystals', they're more or less powder these days rather than the solid chunks they used to be. Wonderful stuff, household soda - a hot solution of just two teaspoons left in a tea stained mug for half an hour or so and the stains just wipe off, like magic. And it got the limescale off my toilet bowl, where the waterline sits, which the 100% toilet limescale remover didn't. Also softens water in the washing machine, means you need less detergent and no limescale build up in the machine either.

I have had some of the new sort, come to think of it. Will runoff be OK on flower beds? Our garden is below the patio and any water runs straight off onto the flower beds.
I use bicarb on stained mugs - just a little on a cloth is magic. No limescale probs here as our water is very soft, which saves lots of work!

Ah, those are not good circumstances for neat application of soda, Steragram. I certainly wouldn't want it being flushed off into my flowerbeds, so I'd not recommend it. When the weather stops being so blasted freezing, with this positively arctic wind, I'm intending to try a strong solution in a spray bottle on a garden wall which is covered in algal growth. The soil beneath is planted, but I'm hoping just spraying it on there might kill the algae, but be insufficient to damage the plants beneath. I'll let you know if it works!

Good luck with that then. It ought to be ok - shouldn't think a spray would produce enough for serious run off.
I made a start on the patio with Eco washing up liquid, warm water and a stiff brush and I was surprised how much it shifted. Tired me out though!