I'd think 18" to 24" should work in most cases.

Coming to your question from an 'historic' point of view.

Several decades ago, in January, east Tennessee had the coldest temperatures in the continental US. For three days the temperatures were below 10F and down to -18F.

This froze the roots of many plants and from what I've heard no Hybrid Teas survived. Some ramblers did survive but the depth of freezing wasn't as bad as near Asheville (where waterlines froze three to four feet down) and here where pipes 24 inches deep had to be replaced.

I think 24" would control most of multiflora parentage and wichurana (based on a survivor that had huge stones above it) and survived many places (Gardenia) could be a shallower spreader.