I know that downloading stuff (such as movies) to an SSD is a bad thing; but if I download them there first and then move them to an external hard disk drive is it a bad thing?
If you're worried about the life of your SSD, if it is a fairly modern model you shouldn't have any issue.
For example a few months ago techreport did a test with modern SSDs. In the test the SSDs died after writing at least 700TB up to more that 2PB. If you plan to write about 100GB per day on your disk it means at least 20 years of life.
It first depends on your definition of 'bad'. ..but if that definition is 'anytime I write to my SSD' then it makes no difference whatsoever whether you keep it on the SSD or move it somewhere else afterwards.
Of course, you could skip the entire 'danger' scenario, if you feel the need, & save it to the external in the first place.
To the essence of the question: If you believe that downloading to an SSD is bad because of write cycle issues...then downloading to an SSD and moving to an HDD will not make any difference at all. Consider that the data still has to be written to the SSD in the first place, before it is then moved off to the HDD.
However, as other posters have said, unless you're doing some type of massive data-logging application (example: surveillance cameras) where you're writing hundreds of gigabytes per day to your SSD, then you're highly unlikely to actually wear out your SSD in the near or even somewhat distant future.