so, how are you running your outboard while towing for it to ingest dirt?
I have an outboard manufactured by Gale in 1956 that has been towed up and down gravel roads thru-out northern Wisconsin and the UP for at least the past 35 years with no ill-effects other than needing to wipe the dust from the outside of the cowl.
If it's an outboard motor, and dust is getting under the hood of the motor, and getting your powerhead and everything else under it dusty, just get a dust cover made for the motor or a generic dust cover with elastic around the bottom of it to keep the dust out. Simple solution. If it is getting into the engine itself, I am with Scott on his reply. How are you running the motor while towing the boat???