Yes, when Ennis and Jack are on their last camping trip on the evening when Jack says he misses Ennis so much "he can hardly stand it"... they're shown passing a bottle of whiskey back and for that has an "Old Rose" label on it.
Well, there are real brands out there with the world "Old" involved. There's Old Crow, Old Whiskey River, Old Overholt, Old Rip VanWinkle, Anchor Old Potrero and Old Granddad. The only one of this list I've tried is Old Granddad (which is incredibly strong, 100 proof!). But, truly, as far as I can tell there's no current version of Old Rose out there on the market (unless I'm just totally not hitting on it doing google searches).
More research on this would be great!
I could swear I once found a photo on Google images of a whiskey bottle labeled Old Rose. But in subsequent searches, I've never been able to find it.
I just did a Google search of "Old Rose" and "whiskey," and the first thing that came up was this page!