Basically you have someone each day that doesn't ride but instead drives a big car, a pickup truck or an SUV etc. to the next hut we all sleep in. The car is loaded with the luggage and food for everyone.
On the traditionally ridden trail rides for long trips there are old sheepherd huts at roughly a days ride apart all over the place and you can book a night there. There are also usually a big fenced in area for the horses near each hut. Sometimes there's enough grass but otherwise you'll have to bring in or buy hay from the hut.
You ride with atleast 3 horses per person and drive the spare horses with you in a herd. Say you've got 10 people, you've then got maybe 35 horse so there's a herd of 25 'extra' horses that needs to be driven along on the trail ride.
Then every few hours you stop the herd (sometimes just in a 'corral' made out of humans holding white electric fence type ribbon between each other) get a fresh horse and relax a little bit.
When you get to the hut you'll sleep in the car is already there and everyone then goes to prepare food etc. If it's a commercial trip you'll pay and the people in charge will do the driving, if it's just a bunch of friends going on a trip like that you might have someone along that doesn't want to ride but wants to be on the trip nevertheless or you take turns each day, who'll be the unlucky driver for the day.
Icelandic horses are kept in herds a lot so it's usually not a problem gathering horses from all over the place and driving them together in a herd and then also keeping them together in the fenced in area overnight.
The biggest trip I've been in like that had around 100 horses, there were roughly 20 people riding, all from different areas and different stables, bringing around 5 horses each, so the horses didn't know each other at etc. but it all worked out, the horses know their 'herd etiquette' so that's hardly ever a problem.