Mine was last trimmed in October and is barefoot having never been shod. Having said that he tripped and feel the other day so when our farrier was at the yard I got him to file off a little split but it wasn't necessary
Mine goes 6 weeks in summer, 8 in winter. I find in summer his feet grow very quickly, but in winter it slows right down. In winter, sometimes there's not much growth in 8 weeks, and he mainly needs re-shoeing, but in summer he grows very quickly and can lose shoes if we're not on top of it.
I have 2 barefoot ponies. Farrier came yesterday, after 12 weeks and said neither pony needed doing. She tidied them up a little with a rasp and booked in again for 16 weeks time.
Varies according to need. Barefoot and ridden almost every day on a mixture of road, stony track, grass, and sand school. Through the winter months it's probably every 3 months or so (mainly because I'm worried about balance, as he wears his hooves, particularly the hinds, unevenly. He's broad - but goes very close behind so wears the outsides. If I could get the trimmer to put hoof ON, I would!). Usually, there's nothing more than a few shavings to come off, and my trimmer is actually quite happy for me to tidy up the odd chip myself - so I probably don't need her at all in winter to be honest. Currently having to boot for longer road stints, as he's wearing so much hoof with all the roadwork (fields waterlogged).
Summer there's more off road work, and he grows more foot, but every 10 weeks is still ok. He's sound as a pound over all surfaces and his feet are like mahogany.
If they have shoes on then every 5-6 weeks religiously.
If they don't have shoes on then it completely depends on the horse. I have two with front shoes and unshod behind at the moment, tbh they don't really need a great deal of trimming behind - they get a quick tidy up when fronts are done but both horses seem to keep their hinds in good order without any great need for intervention.
I've got one retired and unshod. He gets a tidy up approximately every 10 weeks - there wouldn't be anything the farrier would want to do every 5 weeks! This is a horse with a long history of front feet issues and they look better now than they ever have before.