Cold temperatures CAN cause a runny nose with clear discharge. Cold air causes the nasal mucosa to vasoconstrict and dry out, triggering a cascade of events that eventually results in increased mucus production by the nasal mucosa to protect itself from further damage by the cold air. Thus cold weather --> serous nasal discharge. The same thing happens in people.
However, a clear discharge does NOT mean the horse is cold if the ambient temperature is comfortable. A variety of things can cause clear discharge - dust, allergens, high ammonia levels, low ambient humidity, foreign body reaction, mild respiratory viruses etc. etc. etc.