See, I think the first priority was to get the saddle off Gunny with no thought or reason to photograph. Jmo
Hopefully RCMP put their best detectives on this case.
I do not think that was a priority - to remove the saddle. I think the first priority was to identify who the rider/owner was.
In my opinion, the tack would have been left in place, until they (ranchers, loggers) determined where the horse belonged.
I do not believe KR would loosen the cinch on a spooky, jumpy horse in the dark. You wouldn't loosen the cinch on a jumpy horse & risk the saddle moving & adding to the horses stress. I have more thoughts on that but it has not been released on MSM.
The most convenient way to carry that saddle around while trying to figure out who's horse this was, would have been to leave it in place on the horse. We know the saddle was not damaged, and his horse was not injured (there are MSM reports & quotes from NR stating the saddle was not damaged in any way, & the horse was unharmed, aside from being spooked).
On that Monday, after KR contacted local ranches and ranchers were handling the horse and trying to find the owner, they would assume the owner was searching for his horse, leave as much of his gear as possible in place, and go about locating the owner.
This would start with gathering a detailed description of the horse & gear. Photograph it and start sharing information, asking who's horse it was. They would look for an identifying brand on the horse, and take a photo of any existing brands and markings, and tack. In my opinion, The ranchers would not have separated the saddle from the horse, most likely, until the horse was about to be loaded into the trailer, or even until after the horse was unloaded and returned to NR. Folks who spend a lot of time in the saddle often haul with tack on, so it's very possible the horse returned to NR with the saddle still in place on BT's horse.
I could see the headstall (which holds the bit in place for those who don't know) may have been removed and replaced with a halter, or had a halter placed over it (depending on which bit was in place - BT used a few different bridles/bits) for use while hauling the horse back to NR, but, again, I strongly believe the tack was left as is and documented. This would have been done initially (among other reasons) so that local ranchers who were trying to identify the owner could quickly pass a description of the horse & it's tack around, (brand, type, details, etc.) to locate where the horse should be returned to, or who should be contacted to come pick up the horse.