Depending on the age and amount of dirt in the cobwebs, sometimes you can blow them down with a leaf blower. I have an electric blower, which has a LOT of power. Look for the MPH it can do, to get the powerful ones. I don’t want to be running gas-powered tools INSIDE the dusty, dirty barn with many flammable things (hay, straw, shavings) inside.
Other idea is the extendable pole, with duster head (Webster) screwed on the end, to snag dirt and cobwebs in high places.
CHANGE THE LIGHTBULBS, get the dirt off them. If possible, put on the glass cages to prevent dust landing on warm bulbs for spontaneous combustion in the future. Florescent bulbs can have the clear tubes put on which keeps dirt off and will catch glass if bulbs get bumped and shatter. I got my tubes from Home Depot, many sizes to fit bulbs.
Shop vac might be helpful, in pulling dust down, sucking up cobwebs. I did have to use several tubes to reach upper places.
Do wear a paper mask, hair covering and safety glasses or goggles to keep the floating dust and dirt out of your lungs and hair. Can get very filthy to be breathing that nasty stuff while cleaning. Mouse dirt vaporized, gets me choking and sneezing, so the paper mask helps a great deal. No telling WHAT kind of germs that has in it!!
Good luck cleaning. Get a couple good size, ABC rated Fire Extinguishers to hang by the entrance doors of your newly cleaned barn for Safety.
