I assume you do not mean that the path is icy - it was about -5C last night. If the path is slippery with moss then you can get stuff from the garden centre to treat this.

I still go for hot water and a good stiff brush and elbow grease. failing that you could use a power washer or by path cleaner from the gc or diy store.

I use 2 different methods to get rid of the green stuff on my flag paths: if there is only a small area to do near the house/water supply I use a very powerful pressure washer and it blasts the flags clean - I probably do this twice a year. Anything further away that the pressure washer can't reach I use a solution of Jeyes fluid, a stiff broom and some hard brushing. I don't mind this job as I love the smell of Jeyes!

I use a product readily available from garden centres called Algon. It can be applied with a very fine rose from a watering can or by knapsack sprayer. If you treat your area when it will be dry...... for a few days it will do the job well . Be patient as it takes a couple of weeks to take effect and as it is organic it does no harm to surrounding plants. It continues to work slowly for months.