A couple of centuries ago it would almost always have been the three remaining cookies (except cookies wasn't very common then! :) Probably because back then schoolteachers were more likely to be (prescriptively) telling their pupils how they should speak (see this webpage, specifying that adjectives of Quantity or Number come before Quality or Opinion).
But some aspects of usage have changed over time, even though not many grammar books will have been updated to reflect this....

Personally, I've no particular preference for OP's exact example, except to point out that I'd probably choose to put the contextually more important adjectival element last. It feels much more natural for me to place heavy stress on the final adjective before the noun, so if I wanted to call attention to the fact that there were three (not just one or two, and certainly not half-a-dozen or more), I'd say the remaining three cookies (with the highlighted number being spoken more loudly). As an example context...
I brought a dozen cookies out to the adults' table, but most people said they were full up, so I took half back to the kitchen straight away. Mr & Mrs Smith politely ate one each, and Mr Brown slipped one to the dog under the table. Children ate the remaining three cookies.
...where the "emphasis" (such as it is) might be partly "justified" by the fact that I've effectively been guiding my audience through a slightly complex bit of arithmetic, wherein "three" is the final answer.