The operation, involving helicopters, was scheduled to get under way early today (NZ time).
The Bureau of Land Management said members of the public were welcome to watch the operation, near Susanville, by joining an escorted tour. Participants must provide their own four-wheel-drive vehicle.
"The bureau is planning to provide public observation of roundup operations daily so long as the safety of the animals, staff, contractors and observers is not jeopardised and operations are not disrupted."
It said it intended to have the corrals open to the public every day during the operation.
The bureau says the appropriate management levels for horses in the Twin Peaks area is 448 to 758 horses and 72 to 116 burros.
Current estimates indicate there are 2303 horses and 282 burros in the area.
"Based on current estimations, the bureau would attempt to gather up to 2300 horses and up to 210 burros from the Twin Peaks area."