While I eventually managed to remember the actual names for the last three months, I just could not remember which was which, until I noticed this. Here's my weird way of remembering the order Hydref, Tachwedd, Rhagfyr.
HTR - as the months get colder, you need a HeaTeR. HTR. That's it! Maybe it won't help you depending on how your mind works, but it now always works for me!
What's the story behind the word "Rhagfyr"? It's easy to remember as the last month as it could have things in common with "Ragnarök" (the end of the world in norse mythology) and the old Swedish word "fyr" is a fire producing smoke (the Swedish word for smoke is "rök"), but I doubt very much that this is the correct concept... :-)