Had the same idea - not with doom - but with a Quest 3D and watching videos of me riding in the summer. First make a film using an 3D camera (something like a Insta360) and then view that on the Quest in winter while riding exercise bike.

Video speed would sync to the exercise bike speed, giving a feeling of reality.

The core problem is that sweating inside a Quest isn't a good idea ...

I did thrill of the fight a lot back during the pandemic. sweating in a quest isn't ideal, but it's not unmanageable for brief periods of time (15-30 minutes). The only real problem is that the lenses can get sweaty or foggy and all of a sudden I go from punching faces and dodging fists to punching at blurs and failing to dodge other blurs.

Maybe instead of a quest you just display video to a screen? When I was using a hotel fitness center they had a peloton and that seems to be something you can do with those. It was a couple years back and I recall the video being loosely if at all tied to the speed you pedal at, but it was more fun than just looking at a wall while I pretend to go somewhere.