If you armor up, let 99% of the air out of your tires, & drag the rear brake while pedaling, riding icy trails can be a fun challenge. I spent over 30 minutes sessioning this corner on CROCT's Sechler Pk trail this week. After a dozen+ fails, I was able to make it up 3 times: once cheating to the left, once cheating to the right, and once right up the middle.
We had a lot of rain on Xmas here in southern Minnesota that completely ruined our several inches of fluffy snow. But as the temps dropped, the melting snow froze, creating some unusual ice. I found this mini-skating rink near my house that coated a sidewalk, curb, and access street. The gradual slope made it an ideal traction challenge. I kept tightening my approach to make it more difficult. I'm using ratcheting, track stands, and rocking skills. And you'll see the difference between tires inflated at 10 psi vs 1-2 psi. But the main technique I deployed was to constantly apply the rear brake with just enough pressure to prevent any wheel spin. I call it 'dragging' the rear brake since that seems to best describe it, ie, applying steady power/pedaling while the brake is engaged just the right amount. I learned this technique riding mototrials, most typically on slippery off-cambers where steady power via the throttle while dragging the brakes could help prevent the rear wheel from slipping out underneath you. 1-min video, no slowmo: