I'm pretty confidence that most of you empty your house and start dumping them in your new home or you just leave it there.
What do you do?

I Empty my new house and put the items in my newly built one. It usually takes me several trips though.

Get everything you can, get in a horse, fast travel and you can say good bye to your old house. (My carry weight is like 146756/550)

Ah I did not think of this thank you. And my carry weight will also be huge

I'm dreading the thought of it but eventually i'll travel up to hjerim and get all my stuff, the only time i've moved prior to this is from breezehome to hjerim and when i did that i just left a few of cheap decorations that I had put there and the majority of the junk that i'll never need. Probably do the same in this case

easiest way i've found to move is to just grab everything from the old house, get on my horse, fast travel to the new house and make the slo mo walk inside lol