We have several bushes of Mme. Antoine in coastal SE Virginia (8A). Unseasonable cold in early January this year, an abrupt temperature plunge. Many of our Chinas had damage but Mme. Antoine had the most-- all 3 bushes had to be cut back almost to the ground.
We normally don't have to winter-protect our teas but I will at least mound mulch at the base on this one.

I've not found any reference to a climbing 'Mme Antoine Mari' sport in any of the catalogues or rose literature seen so far. But Teas do have that tendency to push out very long growth to get their heads into the sun - and the more established the rose, the more often you see this sort of growth, especially where the rose has something to lean against - a support, another rose or a wall. Competition for space or light results in some mighty growth.
My Mme Antoine Mari has stayed reasonably shrubby so far - but it is in a very open position. In other parts of the garden, Safrano uses General Schablikine for a leg-up and makes very long growth. They get good morning sun but are in semi-shade from a bank of trees in the afternoon. And G. Nabonnand and Mons Tillier use each other as support to reach for the sky.
A local foundling we call "The Gill Rose" which is the same as "Octavus Weld" - usually grown as a shrub, grew 20 feet up a windmill trying to beat Honeysuckle to the sun and other roses we think of as shrubs of 2-3 metres in height are known to have scaled 2-story buildings in colder places. I think it's fascinating to see what Teas can do given time, opportunity, necessity and something to lean against.