I am trying to tie up a loose end in a book that I am writing and have been unable to find any information about Iraqi access to television in the timeframe. I understand it would be possible to see cartoon's in Kurdistan if that was an option to citizens. I also know in 1986, Iraq had only two government ran television channels. Other means that might have been available that I am not familiar being a possibility is through recorded VHS tapes. Having been to Iraq several times, I know there is a strong black market for video's, I am not sure if it was the same during Saddam's rule.
The late 80's is around when you would have started to have the first penetration of satellite television into the Arab world. It was slow going and if you're looking at 1986 in the Iraqi KR I suspect there would have been been few to no dishes. The need to find out reliable news from CNN about the buildup to the Iraq war was a major catalyst for the introduction of satellite tv in the region.
In terms of western cartoons, I think you'd have been unlikely to find them. Tom and Jerry is a perpetual favorite for international export markets because it's largely non-vocal/non-written, and physical comedy works well the world over. It's been airing in Egypt for decades, for instance, though I can't say with certainty that it would have been on in Iraq.
I'm afraid I'm less familiar with what kinds of cartoons might have been produced domestically in Iraq or regionally for consumption in Arabic/Kurdish, or whether VHS tapes would have been viable.
You might actually be better off cross posting this to somewhere like /r/arabs, or /r/kurdistan. I've done a good bit of research into Arabic media but the availability of western cartoons in 1980s Iraqi KR is just not something I've come across.