My storehouse is full of pasture, but it is still not enough for feeding my cattle and sheep through the whole winter; while processing the pasture, it is full of dust. How can I deal with this problem?

Make your pasture/hay/herbage into biomass pellets by biomass hay grass pellet making machine. Hay can spontaneously combust when stored with too high of a moisture content. It also takes up a lot of space. Pellets are safe from combustion and are more compact. You don't need a whole loft or shed to store them.