Angus1895: Two "campgrounds" inside the city limits of Dillon, Montana.
One is a K.O.A. and the other I believe is called "Riverside Campground - they MAY have room/facilities for Mules?
There is another campground about 3 miles south of Dillon near the junction of I-15 and Montana State Highway 278 - this campground is 200 yards west of I-15 on Highway 278. This campground would probably have a better chance of being able to accommodate Mules.
Also just west (somewhere) of this campground is a facility dedicated to people travelling with horse who need accommodations for horse/mules and small cabins to house the humans.
I hear people talking about it but don't know exactly where it is.
I wish I could be more helpful about this facility - I have an afternoon Hunt planned today but will do some checking for you on that horse/human facility.
Good luck on your hunt.
There are lots of free campgrounds around Dillon for humans to camp but I am not sure about the welcomeness of Mules?
Pardon my slow reply - I did not notice your posting til just this minute.
If you are interested in Hunting south east of Dillon the East Fork of the Blacktail Campground has room (but no corrals!) for Mules - its about 20 miles SE of Dillon.
Which direction from Dillon are you interested in Hunting?
The Campgrounds that "Driftboater" mentions above are actually on the "Bighole River" not the Beaverhead River - I don't want you to get turned around.
Those are nice campgrounds but again I am not sure if Mules are welcome there?
Again good luck.
Hold into the wind
VarmintGuy