Its worth remembering that, if your gear is reasonable for the climb, climbing on a fixed gear is considerably easier than climbing on a freewheel bike.
Geared bikes obviously have more bail-out gears, but your fixed drivetrain pulls your feet through any dead spots in your pedal stroke.
A fixed gear rider will be doing less work and fatiguing fewer muscles than a geared rider using the same ratio.
Fixed gears are cool, but not cool enough to defy basic physical laws. Perhaps you are confusing fixies with unicorns.