treat potash like lime. Yes, keeping it dry does easy the spreading.
Leaving it in the fire pit & it will wash away.
You should use it like compost, in that you cut it in where you will plant next season. You need a soil test to find out if you need it. Do not put it near Blueberries,Rhododendron, Azalea or any other low pH(sour)loving plant. This site & the net can help you find what plants need more potash.

Keep in mind that wood ash is largely Calcium Carbonate, Lime, much smaller amounts of Phosphorus and Potash. The nutrients in wood ash are very water soluble which is why it needs to be kept dry, so the nutrients in the wood ash are not washed out before being placed where they might be needed.

Here is a link that might be useful: Nutrients in wood ash

Let's keep the terms straight, you are asking about 'wood ashes', not potash.
While such ashes contain some potassium, we shouldn't intermix the terms as though they are the same, they are not.

Wood ashes, like any other soil amendment or addition, should be used with care and thought about what it's value is to the soil and what plant/s it might bnenefit.
Since the ashes are about 50% nutritive value of lime, it should be not used where acid plants grow, including trees, shrubs and evergreens.
The source of wood ashes too are important, especially if put around food gardens. Some woods contain harmful metals which can poison the soil.
A gallon of wood ashes is about the most that should be spread on an area of 10 sqare feet. It should be well mixed with the soil and watered in.

Instead of waiting for spring, spread the wood ashes over your lawn and let the snow take it down.
Use the ashes to draw the sun to plants affected by ice storms and is a great melter of snow and ice on walkpaths.