I would plant it in a deep pot where the roots can establish well.
It will be problematic in heat and dry weather to attempt growing it in the open garden.

I don't know about root cuttings.

I grew up in Aurora, now live in SC. I cannot imagine that a clematis would survive a colorado winter in the ground. You might ask your local nursery if you don thear back from any experts that live where it gets that cold and dry.

Clematis will tolerate cold just fine if it's established, which is why planting it in the fall is not the best idea. I am getting close to 100 clematis plants in the ground over here and never lost any to cold, even after temps close to 30 below zero. If the plant is of a fairly good size, I'd put it in the ground right away. Make sure it's planted deep - a few inches lower than it was grown before, water, and mulch, mulch, mulch. 3-4" of mulch will save you a lot of waterings.
You can't propagate clematis from root cuttings. Unless there's a stem with a leaf node attaches to those roots, they won't grow. Sorry. Good luck with your new addition!
Grow

Many Clematis - including Nelly Moser, grow just fine in Colorado at 6500 feet plus: I have dozens of them.

If you haven't put it the ground just yet, I'd look for a spot that gets full morning sun - they seem to do the best with that aspect. The west side of buildings just gets too hot come July. Ideally, plant it by a down spout so it gets winter moisture from melting snow on the roof.

I have planted clematis in both spring and fall (as late as after a killing frost) in my similarly cold zone and had them survive without any issues. My greatest problem is keeping plants alive in pots all summer, but if you can do that, you would be fine with it in the ground giving it the same careful care.

I agree with growdarnit, if it has good roots plant it in the ground where you want it and be vigilant about keeping the soil moist. If you decide to pot it up dig a hole in a holding area and put the plant, pot and all in the hole which will help keep soil moist and temperatures moderated. I have a holding bed for seedlings and newly bought potted clematis waiting for a permanent location, where all are in the ground. This holding bed is in an area close to water and where I see it daily so they don't dry out. When you are ready, pull the pot out and plant.