The chief and most ancient road suitable for wheels, ran from the greatest port, Rómenna in the east, to the royal city of Armenelos, and thence on to the Valley of the Tombs and the Meneltarma; and this road was early extended to Ondosto within the borders of the Forostar, and thence to Andúnië in the west.
Along it passed wains bearing stone from the Northlands that was most esteemed for building, and timber in which the Westlands were rich.
- UT; The description of the Island of Numenor
"If I return, I say: but be assured that I shall return, for the keeping of my oath, unless disaster befall us and I perish with my people on the long road. For that must be on the east side of Anduin ever under the threat of Mirkwood, and at last must pass through the vale that is haunted by the shadow of the hill that you name Dol Guldur.
On the west side there is no road for horsemen, nor for a great host of people and wains, even were not the Mountains infested by Orcs; and none can pass, few or many, through the Dwimordene where dwells the White Lady and weaves nets that no mortal can pass."
- Eorl's words and we are never told his folk used wagons in war, UT; Cirion and Eorl
Horsemen were galloping on the grass of Rohan; wolves poured from Isengard. From the havens of Harad ships of war put out to sea; and out of the East Men were moving endlessly: swordsmen, spearmen, bowmen upon horses, chariots of chieftains and laden wains.
- again a distinction between chariots and wains as seen before with teh Wainriders, I dare to assume it's a matter of tross
From FotR;
Many roads and tracks crossed the green fields, and there was much coming and going:
wains moving in lines towards the Great Gate, and others passing out. ...
On the ride horsemen galloped to and fro, but
all the street seemed to be choked with great covered wains going south. But soon Pippin saw that all was in fact well-ordered:
the wains were moving in three lines, one swifter drawn by horses; another slower, great waggons with fair housings of many colours, drawn by oxen; and along the west rim of the road many smaller carts hauled by trudging men.
- Gondor did not use wagons in war and they are not associated with warriors here, RotK; Minas Tirith
It was Gandalf that brought the first tidings. With a handful of horsemen he came in the middle morning,
riding as escort to a line of wains. They were filled with wounded men, all that could be saved from the wreck of the Causeway Forts. (...)
All day the labour went forward, while the men of Minas Tirith looked on, unable to hinder it. And as each length of trench was completed,
they could see great wains approaching; and soon yet more companies of the enemy were swiftly setting up, each behind the cover of a trench, great engines for the casting of missiles.
- again they are simply tools of transportation, RotK; The Siege of Gondor
Merry was summoned and rode away with
the wains that took store of goods to Osgiliath and thence by ship to Cair Andros;
- RotK; The Steward and the King
Then
they laid the bier upon a great wain with Riders of Rohan all about it and his banner borne before; and Merry being Théoden’s esquire rode upon the wain and kept the arms of the king. (...)
And Éomer said: ‘
Kings of old would have laden you with gifts that a wain could not bear for your deeds upon the fields of Mundburg;'
- RotK; Many Partings