Tents, to be linen or not to be linen.

[Caballo]

And in addition, as quoted above from Ammianus "quia nex sarcinale iumentum quisquam nec tabernaculam habuit, praeter principem, cui tapete et sisyra suffecerant pro tentorio"- using tabernaculum and tentorio for tent, not sub pellibus.

Its worth looking at the derivation of the word to get closer to what it may have meant to the Romans.

1/ Tentorio- Etymology of the Latin word tentorium
the Medieval Latin word tentorium (tent)
derived from the Latin word tentus
derived from the Latin word tendere (to stretch; pitch tent, encamp; pull tight; stretch, spread, extend)

Nothing to do with leather- everything to do with stretched material.

2 Tabernaculum- diminutive of taberna "hut, cabin, booth".

Taberna (tavern, inn; wood hut)
derived from the Latin root *traberna
derived from the Latin word trabs (tree trunk; log, club)

Again, nothing to do with the material, and everything to do with the shape.

I think the evidence both written and illustrated points towards leather and other materials being used for tents- including linen, and in necessity, woollen blankets.