When can you hunt them with muzzleloaders?
That depends.
I can only speak specifically about Idaho, because I just applied for tags here so I have all the lit in front of me. Generally, I believe Utah is similar, though.
Here in Idaho, it depends on the region. The state covers a good amount of latitude, and elevation varies from 770 to 12,662 feet above sea level, with everything in between well-represented.
Some special muzzleloader and archery seasons are during the rut, when the elk can be called in. Some people are damn good at it. This guy is a competitive elk caller:
Others are very late, when snows typically drive elk down from the mountains.
There's a distinct difference between hunting elk in the background, and in the foreground, of this picture (Sawtooth Mountains here in Idaho).
They have an effective range of about 150 yards. Some perhaps a bit more. Do you advise people not to hunt elk with a muzzleloader as well?
There are special muzzleloader and archery seasons, like I said.
Typical general rifle seasons are about 3 weeks long, in between the rut and the snows, when the elk are often in the high mountains, and have nothing to do but eat and look out for hunters.
Furthermore, that's when greater numbers of hunters are running around, taking 300 yard shots. It's usually AFTER some other seasons (archery and/or muzzleloaders) have started. So the elk aren't exactly going to be caught off-guard very easily.
If this were 1909 instead of 2009, the seasons were long and hunters sparse, it probably wouldn't make any difference. But in 2009 in the real world, it does.
People hunt and take elk with muzzleloaders and bows every year. But during general rifle season on public land? Not so much.
If someone has access to a very large tract of private land that is not ordinarily hunted at all (a few people are so lucky, but not me), general rifle season might be viable with a short-range firearm. There are also public areas where only short-range firearms are allowed during regular season here.
In Idaho, a .30-30 is not
legally a short-range firearm, so that would not be any help.
Hunting elk in the mountains is not like hunting deer in the low country.
Now there are some depredation permits available, where you
might be able to take pot shots at elk when they come down to feed off crops. That's a possibility.
But for
general seasons, an earnest look at the calendar and a topo map would be pretty daunting to someone who wants to shoot an elk at 75 yards -- at least anywhere around here.