I have driven almost everything in the Ouray/Telluride area in my 4Runner and my former 6 cyl Outback so if you are more specific maybe I can share observations.
As a general rule of thumb, that particular area is extremely overcrowded which means that the least capable vehicle will create long lines and not everybody will be pleasant to its driver.
Though I have taken my Outback on true 4x4 trails, it would not even cross my mind to take the Model Y on anything beyond a dirt road. I doubt the X is any more capable in any way.
I guess I would drive the Y on Stony Pass from the west side to the creek crossing and back. It is really just a narrow glorified dirt road except for the water crossing. Other than that, nothing comes to mind. Just the last several miles of the dirt road into Animas forks will seriously test a Y or X let alone the trail from there into the actual easier passes.
Corkscrew is smooth but can have ruts and serious holes due to weather damage or UTV/ATV damage as well as long lines. Under ideal conditions, I might consider it but...not really
Hurricane Pass is very mildly rocky and combined with California could make for a truly adventurous for a Tesla loop (easy in my former Outback) but it would take giant balls of gold, I think (a Steve Vai song title).
HERE ARE ALL THE ISSUES:
--Non existent rocker panel clearance;
--HORRIBLE wheels when it comes to offroading unless you can get 18" wheels.
--Extremely low hanging front bumper that is just asking to be ripped off
--Minimal ground clearance and a battery right there.
--Problematic rear bumper.
I guess traction wise the Tesla will be fine on many of those trails but it is not traction I would worry about.
Mind, you I have a 4Runner on desert suspension with 12.5" of ground clearance, Mickey Thompson MT tires, and a full set of 3/16" steel armor + rock sliders so I am pretty spoiled nowadays so there is that.
I know Jeep rentals are pricey and as a former Subaru offroader I hate recommending a rental, but an open top Jeep on slow going trails is unbeatable. Here, on the majority of desert trails, I can fly past the Jeeps with my suspension but on slow going mountain trails, they are just fantastic.