Those roses in existence before 1867 -- antique roses and species (wild) roses. Also referred to as Heritage Roses.
[From Gardening with Roses, by Judith McKeon, p. 15:] Old Garden Roses ... are further divided into two categories. Gallica, damask, alba, centifolia, and moss roses are all derived from a common ancestor, Rosa gallica, and are, for the most part, once-blooming. China roses and the China-influenced roses of the nineteenth century make up the other group. These are mostly repeat-flowering, and include the period roses China, Bourbon, Noisette, perpetual damask, hybrid perpetual, and tea roses.
[From Ibid, p. 17:] The old roses bloom in early summer with no repeat flowering (except for 'Autumn Damask', R. damascena var. bifera). Most are extremely hardy, disease-resistant, prickly, shrubs that grow and thrive with little attention from the gardener. They range in height from 3 to 6 feet (1 to 1.8 m) tall and their flower colors range from pure white through blush pink, deep pink, and rose to crimson, purple, and magenta. Bicolored and striped flowers, which are beloved for their novel effect, are found chiefly among gallicas.
[From The Rose Bible, by Rayford Reddell, p. 19: Antique Roses are] comparatively disease resistant (except for inevitable mildew)... not fussy about the soil they're planted in.
[From Gardening at Sissinghurst, by Tony Lord, p. 51:] It must be owned that not everyone loves the old roses. All too often, for each perfect bloom there are three or four in a state of ugliness, their blooms withered or balled with grey mould. Their foliage is undistinguished, their habit ungainly or at best amorphous; unless their pruning is exemplary, their blooms can be few and fleeting. Rosarians and romantics like Vita [Sackville-West], are oblivious to these faults and see only the flawless blooms. But with perfect cultural conditions, pruning and training, the defects of the old roses can substantially be overcome.
[From The English Flower Garden, by William Robinson, p. 620:] generally speaking, Summer Roses, as compared with those that flower right into the autumn, are hardly worth a place [in the garden]...
[From The Admirable Old Roses, by J.R. Carabin, p. 194:] Mrs. Fredrick L. Keays, who wrote that charming book, Old Roses, defines an old rose as one of a type and class differing from hybrid teas and grown in gardens before 1880... Many of the old roses have a fragrance unsurpassed in modern roses...
[From Roses of America, by Stephen Scanniello and Tania Bayard, p. 58:] Old garden roses can be divided into two groups. The first group includes those that were cultivated in Europe before the introduction of everblooming roses from China during the late 1700s and early 1800s. In the second group are the Chinas and the roses they influenced, the tea roses, Bourbons, Noisettes, damask perpetuals, and hybrid perpetuals.