2003 EXPLORER OWNERS MANUAL LINKPage 177 of owners manual..
"Driving while you tow
When towing a trailer:
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Turn off the speed control. The speed control may shut off automatically when you are towing on long, steep grades.
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Consult your local motor vehicle speed regulations for towing a trailer.
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To eliminate excessive shifting, use a lower gear. This will also assist in transmission cooling. (For additional information, refer to the
Driving with a 5–speed automatic transmission
section in this chapter.
Page 150 states..
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O/D OFF lamp is illuminated.
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Provides engine braking.
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Use when driving conditions cause excessive shifting from O/D to other gears. Examples: city traffic, hilly terrain, heavy loads, trailer towing and when engine braking is required."There, DIRECTLY FROM FORDs OWNERS MANUAL. It DOES NOT specifically state that you must turn OD off while towing.
Instead it states to turn OD off IF you are experiencing EXCESSIVE SHIFTING form OD to other gears.